AI & ChatGPT searches , social queries for COMPLEXIFICATION LIE-GROUP
Search references for COMPLEXIFICATION LIE-GROUP. Phrases containing COMPLEXIFICATION LIE-GROUP
See searches and references containing COMPLEXIFICATION LIE-GROUP!
Search references for COMPLEXIFICATION LIE-GROUP. Phrases containing COMPLEXIFICATION LIE-GROUP
See searches and references containing COMPLEXIFICATION LIE-GROUP!COMPLEXIFICATION LIE-GROUP
Universal construction of a complex Lie group from a real Lie group
the complexification or universal complexification of a real Lie group is given by a continuous homomorphism of the group into a complex Lie group with
Complexification_(Lie_group)
and complex numbers. A real Lie algebra g0 is called a real form of a complex Lie algebra g if g is the complexification of g0: g ≃ g 0 ⊗ R C . {\displaystyle
Real_form_(Lie_theory)
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
complexification is a simple complex Lie algebra, unless L is already the complexification of a Lie algebra, in which case the complexification of L is a product of two
Simple_Lie_group
Algebraic structure used in analysis
(c-2)} -eigenspace. The Lie algebra s l ( 2 , C ) {\displaystyle {\mathfrak {sl}}(2,\mathbb {C} )} is isomorphic to the complexification of s o ( 3 ) {\displaystyle
Lie_algebra
Group that is also a differentiable manifold with group operations that are smooth
In mathematics, a Lie group (pronounced /liː/ Lee) is a group that is also a differentiable manifold, such that group multiplication and taking inverses
Lie_group
Concept in Lie algebra mathematics
exceptional Lie algebras. If g 0 {\displaystyle {\mathfrak {g}}_{0}} is a finite-dimensional real simple Lie algebra, its complexification is either (1)
Simple_Lie_algebra
Lie groups and their associated Lie algebras
table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness;
Table_of_Lie_groups
group Complexification (Lie group) Simple Lie group Compact Lie group, Compact real form Semisimple Lie algebra Root system Simply laced group ADE classification
List_of_Lie_groups_topics
Correspondence between topics in Lie theory
In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for
Lie group–Lie algebra correspondence
Lie_group–Lie_algebra_correspondence
Lie group whose manifold is complex and whose group operation is holomorphic
(G)=\operatorname {Lie} (K)\otimes _{\mathbb {R} }\mathbb {C} } , and (ii) K is a maximal compact subgroup of G. It is called the complexification of K. For example
Complex_Lie_group
Topological group with compact topology
compact Lie group, then the complexification of the Lie algebra of K is semisimple. Conversely, every complex semisimple Lie algebra has a compact real
Compact_group
Branch of mathematics
nilpotent Lie algebras are analogs of nilpotent groups. The nilpotent Lie algebras are precisely those that can be obtained from abelian Lie algebras,
Nilpotent_Lie_algebra
Group representation
a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of
Representation_of_a_Lie_group
Writing Lie algebra sets as matrices
say, a connected real semisimple linear Lie group G, then it has two natural actions: the complexification g {\displaystyle {\mathfrak {g}}} and the
Lie_algebra_representation
Direct sum of simple Lie algebras
Lie algebra of a Lie group (or complexification of such), since, via the Lie correspondence, a Lie algebra representation can be integrated to a Lie group
Semisimple_Lie_algebra
Group of 𝑛 × 𝑛 invertible matrices
\operatorname {GL} (n,\mathbb {R} )} over the field of real numbers is a real Lie group of dimension n 2 {\displaystyle n^{2}} . To see this, note that the set
General_linear_group
Mathematical group
form and a compact real form; the former is called a complexification of the latter two. The Lie algebra of Sp ( 2 n , C ) {\displaystyle \operatorname
Symplectic_group
Lie group of Lorentz transformations
transformations. Mathematically, the Lorentz group may be described as the indefinite orthogonal group O(1, 3), the matrix Lie group that preserves the quadratic form
Lorentz_group
Group of unitary complex matrices with determinant of 1
unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group may
Special_unitary_group
Representation of the symmetry group of spacetime in special relativity
linear representations of the complexification s o ( 3 ; 1 ) C {\displaystyle {\mathfrak {so}}(3;1)_{\mathbb {C} }} of the Lie algebra s o ( 3 ; 1 ) {\displaystyle
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Mathematical group of loops in a Lie group
Shimura varieties. If G is a compact Lie group with complexification GC, then the smooth loop group LG has a complexification L G C = C ∞ ( S 1 , G C ) . {\displaystyle
Loop_group
parabolic subgroups in the complexification of the compact Lie group, a reductive algebraic group. Let G be connected compact Lie group with maximal torus T
Borel–de_Siebenthal_theory
Subgroup of a root system's isometry group
particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system
Weyl_group
Concept in mathematics
between compact connected Lie groups and complex reductive groups, up to isomorphism. For a compact Lie group K with complexification G, the inclusion from
Reductive_group
Open convex self-dual cones
analytic continuation. Aut EC is the complexification of the compact Lie group Aut E in GL(EC). This follows because the Lie algebras of Aut EC and Aut E consist
Symmetric_cone
said to be a real form of g {\displaystyle {\mathfrak {g}}} if the complexification g 0 ⊗ R C {\displaystyle {\mathfrak {g}}_{0}\otimes _{\mathbb {R} }\mathbb
Complex_Lie_algebra
248-dimensional exceptional simple Lie group
is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for
E8_(mathematics)
The unitary group is the maximal compact subgroup of G L ( n , C ) {\displaystyle GL(n,\mathbb {C} )} . The complexification of its Lie algebra u ( n
Representations of classical Lie groups
Representations_of_classical_Lie_groups
Algebraic construct of interest in theoretical physics
of a semisimple Lie algebra g its complexification as a real Lie algebra of twice the dimension splits into g and a certain solvable Lie algebra (the Iwasawa
Quantum_group
Creating a "larger" Lie algebra from a smaller one, in one of several ways
of Lie groups, Lie algebras and their representation theory, a Lie algebra extension e is an enlargement of a given Lie algebra g by another Lie algebra
Lie_algebra_extension
Map from a Lie algebra to its Lie group
of Lie groups, the exponential map is a map from the Lie algebra g {\displaystyle {\mathfrak {g}}} of a Lie group G {\displaystyle G} to the group, which
Exponential_map_(Lie_theory)
A quadratic Lie algebra is a Lie algebra together with a compatible symmetric bilinear form. Compatibility means that it is invariant under the adjoint
Quadratic_Lie_algebra
133-dimensional exceptional simple Lie group
mathematics, E7 is the name of several closely related Lie groups, linear algebraic groups or their Lie algebras e7, all of which have dimension 133; the same
E7_(mathematics)
Mathematical term
pass to the complexification of the Lie algebra before proceeding.) To see how this works, consider the case G = SL(n, R). We can take the group of diagonal
Adjoint_representation
Subgroup of the group of invertible n×n matrices
subgroup). Every compact connected Lie group has a complexification, which is a complex reductive algebraic group. In fact, this construction gives a
Linear_algebraic_group
Geometric arrangements of points, foundational to Lie theory
theory of Lie groups and Lie algebras, especially the classification and representation theory of semisimple Lie algebras. Since Lie groups (and some
Root_system
In mathematics, a type of algebra
solvable Lie algebras are analogs of solvable groups. Any nilpotent Lie algebra is a fortiori solvable but the converse is not true. The solvable Lie algebras
Solvable_Lie_algebra
{\mathfrak {g}}} that is the complexification of the Lie algebra of K (this fact is essentially a special case of the Lie group–Lie algebra correspondence)
Representation theory of semisimple Lie algebras
Representation_theory_of_semisimple_Lie_algebras
Mathematical theory
tori. A compact Lie algebra can be seen as the smallest real form of a corresponding complex Lie algebra, namely the complexification. Formally, one may
Compact_Lie_algebra
Double cover Lie group of the special orthogonal group
representations. The spin group is used in physics when describing the symmetries of (electrically neutral, uncharged) fermions. Its complexification, Spinc, is used
Spin_group
Generalized matrix decomposition for Lie groups and Lie algebras
is the Lie algebra of a compact semisimple Lie group. Let g {\displaystyle {\mathfrak {g}}} be the complexification of a real semisimple Lie algebra
Cartan_decomposition
First case of a Lie group that is both compact and non-abelian
this passage from real to complexified Lie algebra is harmless. The reason for passing to the complexification is that it allows us to construct a nice
Representation theory of SU(2)
Representation_theory_of_SU(2)
automorphism group of the compactification becomes a complex subgroup, the complexification of its maximal compact subgroup. Both groups act transitively
Mutation_(Jordan_algebra)
(1994), "4.4: Split Real Semisimple Lie Algebras", Lie groups and Lie algebras III: structure of Lie groups and Lie algebras, Springer, pp. 157–158,
Split_Lie_algebra
Construction in group theory
Lie group realizations for the special linear Lie algebra s l ( n ) : {\displaystyle {\mathfrak {sl}}(n)\colon } every connected Lie group whose Lie algebra
Projective_linear_group
Nilpotent subalgebra of a Lie algebra
the complexification of the Lie algebra of a maximal torus of the compact group. If g {\displaystyle {\mathfrak {g}}} is a linear Lie algebra (a Lie subalgebra
Cartan_subalgebra
Mathematical group
particular, the group W acts on the complement of the complexification of the arrangement of its reflecting hyperplanes; the generalized braid group of W is the
Parabolic subgroup of a reflection group
Parabolic_subgroup_of_a_reflection_group
Group of unitary matrices
this group. The unitary group U ( n ) {\displaystyle \operatorname {U} (n)} is a real Lie group of dimension n 2 {\displaystyle n^{2}} . The Lie algebra
Unitary_group
Branch of mathematics that studies abstract algebraic structures
Lie groups using Weyl's unitary trick: each semisimple real Lie group G has a complexification, which is a complex Lie group Gc, and this complex Lie
Representation_theory
the mathematical theories of Lie groups and Lie algebras. For the topics in the representation theory of Lie groups and Lie algebras, see Glossary of representation
Glossary of Lie groups and Lie algebras
Glossary_of_Lie_groups_and_Lie_algebras
Manifold with inversion symmetry
complex vector space. The simplest case involves the groups SU(2), SU(1,1) and their common complexification SL(2,C). In this case the non-compact space is
Hermitian_symmetric_space
Physics-mathematics connection
links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states
Particle physics and representation theory
Particle_physics_and_representation_theory
(pseudo-)Riemannian manifold whose geodesics are reversible
simple Lie group; B. G is either the product of a compact simple Lie group with itself (compact type), or a complexification of such a Lie group (non-compact
Symmetric_space
Algebra of meromorphic vector fields on the Riemann sphere
two fixed points. It is also the complexification of the Lie algebra of polynomial vector fields on a circle, and the Lie algebra of derivations of the ring
Witt_algebra
Type of subgroup of an algebraic group
weight. A Lie subalgebra of g {\displaystyle {\mathfrak {g}}} containing a Borel subalgebra is called a parabolic Lie algebra. Hyperbolic group Cartan subgroup
Borel_subgroup
Integral polynomial
of G, a maximal compact subgroup KR in that semisimple group GR, and makes the complexification K of KR. Then the relevant object of study is K ∖ G / B
Kazhdan–Lusztig_polynomial
Pictorial representation of symmetry
classification of semisimple Lie algebras over algebraically closed fields, in the classification of Weyl groups and other finite reflection groups, and in other contexts
Dynkin_diagram
Group theory theorem
Lie groups. It states that if H is a closed subgroup of a Lie group G, then H is an embedded Lie group with the smooth structure (and hence the group
Closed-subgroup_theorem
some ξ in g*. Another equivalent condition when g is the Lie algebra of an algebraic group G, is that g is Frobenius if and only if G has an open orbit
Index_of_a_Lie_algebra
Lie group of complex numbers of unit modulus; topologically a circle
\rho _{-n}} is equivalent to ρ n {\displaystyle \rho _{n}} . After complexification, ρ n {\displaystyle \rho _{n}} decomposes as the direct sum of the
Circle_group
Mathematical classification
umbrella of root systems. He tried to introduce informal concepts of Complexification and Symplectization based on analogies between Picard–Lefschetz theory
ADE_classification
{\mathfrak {t}}\subset {\mathfrak {g}}} be the Cartan subalgebra (or its complexification t ⊂ g C {\displaystyle {\mathfrak {t}}\subset {\mathfrak {g}}_{\mathbb
Harish-Chandra_integral
Maximal compact connected Abelian Lie subgroup
compact Lie groups a special role is played by torus subgroups, in particular by the maximal torus subgroups. A torus in a compact Lie group G is a compact
Maximal_torus
Isometry group of Euclidean space
groups are not only topological groups, they are Lie groups, so that calculus notions can be adapted immediately to this setting. The Euclidean group
Euclidean_group
Concept in mathematics
as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group. The Lie algebra s l 2 C {\displaystyle {\mathfrak
Special_linear_Lie_algebra
Aspect of loop quantum gravity
Immirzi parameter is necessary to resolve an ambiguity in the process of complexification. These are some of the many ways in which different quantizations of
Lorentz invariance in loop quantum gravity
Lorentz_invariance_in_loop_quantum_gravity
Harish-Chandra's formula. The group G = SL(2,C) is the complexification of the compact Lie group K = SU(2) and the double cover of the Lorentz group. The infinite-dimensional
Zonal_spherical_function
Mathematical process dealing with Lie groups
semisimple real Lie group. g 0 {\displaystyle {\mathfrak {g}}_{0}} is the Lie algebra of G g {\displaystyle {\mathfrak {g}}} is the complexification of g 0 {\displaystyle
Iwasawa_decomposition
Matrices named after Élie Cartan
local symmetry group. The matrix of intersection numbers of a basis of the two-cycles is conjectured to be the Cartan matrix of the Lie algebra of this
Cartan_matrix
Lie point symmetry is a concept in advanced mathematics. Towards the end of the nineteenth century, Sophus Lie introduced the notion of Lie group in order
Lie_point_symmetry
Root system associated to a symmetric space
ISBN 0821828487 Onishchik, A. L.; Vinberg, E. B. (1994), Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie Algebras, Encyclopaedia of Mathematical Sciences
Restricted_root_system
Particular projective representations of the orthogonal or special orthogonal groups
all Lie groups, and for fixed (V, Q) they have the same Lie algebra, so(V, Q). If V is real, then V is a real vector subspace of its complexification VC
Spin_representation
Theorem in representation theory
{k}}} be the complexification of k {\displaystyle {\mathfrak {k}}} . Let T {\displaystyle T} be a maximal torus in K {\displaystyle K} with Lie algebra t
Theorem_of_the_highest_weight
element of a semisimple group G P = MAN is a cuspidal parabolic subgroup of G ν is an element of the complexification of a a is the Lie algebra of A in the
Eisenstein_integral
52-dimensional exceptional simple Lie group
In mathematics, F4 is a Lie group and also its Lie algebra f4. It is one of the five exceptional simple Lie groups. F4 has rank 4 and dimension 52. The
F4_(mathematics)
cones arise in the analysis of holomorphic semigroups in the complexification of the Lie group, first studied by Grigori Olshanskii. They are naturally associated
Invariant_convex_cone
Simple Lie group; the automorphism group of the octonions
In mathematics, G2 is three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g 2 , {\displaystyle {\mathfrak
G2_(mathematics)
Mathematical concept
analog to a Lagrangian subspace is a real subspace, a subspace whose complexification is the whole space: W = V ⊕ J V. As can be seen from the standard symplectic
Symplectic_vector_space
Feature of a system that is preserved under some transformation
described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group). These two concepts, Lie and finite groups, are the
Symmetry_(physics)
Projective plane
The complex Cayley plane is a homogeneous space under the complexification of the group E6 by a parabolic subgroup P1. It is the closed orbit in the
Cayley_plane
78-dimensional exceptional simple Lie group
mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras e 6 {\displaystyle {\mathfrak {e}}_{6}} ,
E6_(mathematics)
explicitly. If two real Lie algebras have the same complexification, and we have a complex representation of the complexified Lie algebra, their conjugate
Complex conjugate representation
Complex_conjugate_representation
Group of flat spacetime symmetries
non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics. The Poincaré group consists of
Poincaré_group
Representation theory
class of groups. If G is a complex semisimple Lie group, it is the complexification of its maximal compact subgroup U, a compact semisimple Lie group. If g
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
Term in mathematics
semisimple Lie algebra and let g = g R ⊗ C {\displaystyle {\mathfrak {g}}={\mathfrak {g}}_{\mathbb {R} }\otimes \mathbb {C} } be its complexification. Define
Satake_diagram
Representation theory of the symmetries of non-relativistic quantum space
Galilean group by the one-dimensional Lie group R, cf. the article Galilean group for the central extension of its Lie algebra. The method of induced representations
Representation theory of the Galilean group
Representation_theory_of_the_Galilean_group
Infinite dimensional Lie group
the Butcher group, named after the New Zealand mathematician John C. Butcher by Hairer & Wanner (1974), is an infinite-dimensional Lie group first introduced
Butcher_group
Relation between Lie algebras depicted as a square
Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated Lie groups). It is named after Hans Freudenthal and Jacques Tits
Freudenthal_magic_square
Symmetric bilinear form in mathematics
is a semisimple Lie algebra over the complex numbers, then there are several non-isomorphic real Lie algebras whose complexification is g C {\displaystyle
Killing_form
Representation of angular momentum tensor product states important to physics
i in these formulas, this is technically a basis for the complexification of the su(3) Lie algebra, namely sl(3,C). The preceding basis is then essentially
Clebsch–Gordan coefficients for SU(3)
Clebsch–Gordan_coefficients_for_SU(3)
an element of the connected component of the Lie group of Lie algebra automorphisms of the complexification g⊗C. The subgroup Gss of G generated by the
Harish-Chandra_class
Unitary representations of a Lie group
(1952). We choose a basis H, X, Y for the complexification of the Lie algebra of SL(2, R) so that iH generates the Lie algebra of a compact Cartan subgroup
Representation theory of SL2(R)
Representation_theory_of_SL2(R)
Algebra based on a vector space with a quadratic form
straightforwardly, but complexification is most often necessary in quantum mechanics where the spin representation of the Lie algebra so(1, 3) sitting
Clifford_algebra
Representations of finite groups, particularly on vector spaces
}\mathbb {C} } is called real ( V {\displaystyle V} is called the complexification of V 0 {\displaystyle V_{0}} ). The corresponding representation mentioned
Representation theory of finite groups
Representation_theory_of_finite_groups
System of partial differential equations used in Higgs field theory
{\text{ad}}P^{\mathbb {C} }} is the complexification of the adjoint bundle of P {\displaystyle P} , with fibre given by the complexification g ⊗ C {\displaystyle {\mathfrak
Hitchin's_equations
Theorem about projections of coadjoint orbits of a connected compact Lie group
semisimple Lie group G. The result discussed above for compact Lie groups K corresponds to the special case when G is the complexification of K: in this
Kostant's_convexity_theorem
Group of matrices with determinant 1
SL(2, R) SL(2, C) Modular group (PSL(2, Z)) Projective linear group Conformal map Representations of classical Lie groups Hall 2015 Section 2.5 Hall
Special_linear_group
{\displaystyle {\mathfrak {g}}} is the complexification of the Lie algebra of a simply connected compact Lie group K {\displaystyle K} . (If, for example
Weyl's theorem on complete reducibility
Weyl's_theorem_on_complete_reducibility
Type of mathematical space
are actually complex homogeneous spaces in a canonical way through complexification.) The presence of a complex structure and cellular (co)homology make
Generalized_flag_variety
Non-tensorial representation of the spin group
bilinear form. If V is a real vector space, then we replace V by its complexification V ⊗ R C {\displaystyle V\otimes _{\mathbb {R} }\mathbb {C} } and let
Spinor
COMPLEXIFICATION LIE-GROUP
COMPLEXIFICATION LIE-GROUP
Female
French
French form of German Amalia, AMÉLIE means "work."
Girl/Female
Australian, Danish, French, German, Hebrew, Latin, Scandinavian, Swedish
Life; Olive Tree; Defense; Protection
Male
Native American
Native American Miwok name LISE means "salmon head rising above water." Compare with feminine Lise.
Female
Scandinavian
Scandinavian form of Old Norse Lifa, LIV means "life."
Female
Yiddish
(לִיבֶּע) Yiddish form of German liebe, LIBE means "love." Compare with another form of Libe.
Boy/Male
Spanish
Is an abbreviation of names like Amalia: (hard working;industrious) and Rosalia:.
Girl/Female
Norse Scandinavian
Life.
Female
French
Feminine form of French Corneille, CORNÉLIE means "of a horn."
Male
French
Old French form of Hebrew Eliyah, ÉLIE means "the Lord is my God."
Female
Spanish
Feminine form of Portuguese/Spanish Eulálio, EULÃLIA means "well-spoken."
Female
Italian
Italian form of Hebrew Leah, LIA means "weary."
Female
French
Elaborated form of French Adèle, ADÉLIE means "noble sort."
Female
Norwegian
Danish and Norwegian form of German Liese, LISE means "God is my oath."Â Compare with masculine Lise.
Female
Hebrew
(לִיבֶּע) Hebrew name derived from the word lev, LIBE means "heart." Compare with another form of Libe.
Female
German
Variant spelling of German Liese, LIES means "God is my oath."Â
Female
French
Feminine form of French Aurèle, AURÉLIE means "golden."
Female
Vietnamese
Vietnamese name LIEN means "lotus flower."
Female
English
Short form of English Elizabeth, LIZ means "God is my oath."
Female
English
Short form of English Elisabeth, LIS means "God is my oath."Â
Female
Welsh
 Variant spelling of Welsh Linn, LIN means "lake" or "waterfall." Compare with another form of Lin.
COMPLEXIFICATION LIE-GROUP
COMPLEXIFICATION LIE-GROUP
Boy/Male
Indian
With long life
Girl/Female
Hindu, Indian
Golden Flower
Boy/Male
Sikh
One who longs for the divine light, Light of the beloved
Surname or Lastname
English (Staffordshire)
English (Staffordshire) : habitational name from Ellesmere in Shropshire, named from the Old English personal name Elli + Old English mere ‘lake’, ‘pool’.
Girl/Female
Latin American
Made of honey.
Boy/Male
Tamil
Padmadhar | பதà¯à®®à®¤à®°
One who holds a lotus
Girl/Female
Indian
Nice, Beautiful, Radiant
Surname or Lastname
English
English : variant of Bottom.
Girl/Female
Muslim
Fame, Nobility, Intelligence
Girl/Female
English
Feminine of Giovanni;.
COMPLEXIFICATION LIE-GROUP
COMPLEXIFICATION LIE-GROUP
COMPLEXIFICATION LIE-GROUP
COMPLEXIFICATION LIE-GROUP
COMPLEXIFICATION LIE-GROUP
v. t.
To read or repeat line by line; as, to line out a hymn.
adj.
To be still or quiet, like one lying down to rest.
imp. & p. p.
of Lie
adj.
To rest extended on the ground, a bed, or any support; to be, or to put one's self, in an horizontal position, or nearly so; to be prostate; to be stretched out; -- often with down, when predicated of living creatures; as, the book lies on the table; the snow lies on the roof; he lies in his coffin.
v. t. & i.
To lie; to tell lies.
n.
An article of food consisting of paste baked with something in it or under it; as, chicken pie; venison pie; mince pie; apple pie; pumpkin pie.
v. i.
To be maintained in life; to acquire a livelihood; to subsist; -- with on or by; as, to live on spoils.
n.
See Lye.
v. t.
To spend, as one's life; to pass; to maintain; to continue in, constantly or habitually; as, to live an idle or a useful life.
v. i.
To lie; to speak falsely.
adj.
To be situated; to occupy a certain place; as, Ireland lies west of England; the meadows lie along the river; the ship lay in port.
n.
Same as Lif.
n.
The position or way in which anything lies; the lay, as of land or country.
n.
Life.
v. i.
To recline; to lie still.
adj.
To abide; to remain for a longer or shorter time; to be in a certain state or condition; as, to lie waste; to lie fallow; to lie open; to lie hid; to lie grieving; to lie under one's displeasure; to lie at the mercy of the waves; the paper does not lie smooth on the wall.
obs. p. p.
of Lie. See Lain.
v. i.
To pass one's time; to pass life or time in a certain manner, as to habits, conduct, or circumstances; as, to live in ease or affluence; to live happily or usefully.
n.
The equator; -- usually called the line, or equinoctial line; as, to cross the line.