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133-dimensional exceptional simple Lie group
In 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;
E7_(mathematics)
Topics referred to by the same term
E7, E07, E-7 or E7 may refer to: E7 liquid crystal mixture E7 (mathematics), an exceptional Lie group, or its Lie algebra e 7 {\displaystyle {\mathfrak
E7
248-dimensional exceptional simple Lie group
series labeled An, Bn, Cn, Dn, and five exceptional cases labeled G2, F4, E6, E7, and E8. The E8 algebra is the largest and most complicated of these exceptional
E8_(mathematics)
Subalgebra of E8 containing E7
In mathematics, the Lie algebra E7½ is a subalgebra of E8 containing E7 defined by Landsberg and Manivel in order to fill the "hole" in a dimension formula
E7½
Set with associative invertible operation
In mathematics, a group is a set with an operation that combines any two elements of the set to produce a third element within the same set. The following
Group_(mathematics)
78-dimensional exceptional simple Lie group
infinite series labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E6 algebra is thus one of the five exceptional cases
E6_(mathematics)
Relation between Lie algebras depicted as a square
(Baez 2002, 4.3 The Magic Square) (Baez 2002, 4.5 E7) (Baez 2002, 4.6 E8) "This Week's Finds in Mathematical Physics – Week 106", John Baez July 23, 1997 Adams
Freudenthal_magic_square
Geometric arrangements of points, foundational to Lie theory
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental
Root_system
Directed graph which is also a multigraph
In mathematics, especially representation theory, a quiver is another name for a multidigraph; that is, a directed graph where loops and multiple arrows
Quiver_(mathematics)
Associator E7 (mathematics) Quadratic Jordan algebra Bertram, Wolfgang (2000), The geometry of Jordan and Lie structures, Lecture Notes in Mathematics, vol
Triple_system
Natural number
because 57 = 2 5 + 5 2 {\displaystyle 57=2^{5}+5^{2}} . The split Lie algebra E7+1/2 has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest
57_(number)
Belgian mathematician
Fujiwara's theorem for equivariant correspondences). Brumer–Stark conjecture E7½ Hodge–de Rham spectral sequence Logarithmic form Kodaira vanishing theorem
Pierre_Deligne
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)
Set of the values of a function
In mathematics, the image of a function f : X → Y {\displaystyle f:X\to Y} is the set of all f ( x ) {\displaystyle f(x)} such that x {\displaystyle
Image_(mathematics)
Complex simple Lie Algebra
dimensions are 14, 52, 78, 133, 248. The corresponding diagrams are: G2: F4: E6: E7: E8: In contrast, simple Lie algebras that are not exceptional are called
Exceptional_Lie_algebra
Branch of mathematics that studies abstract algebraic structures
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of
Representation_theory
Mathematical symbol representing infinity
The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, after the lemniscate curves
Infinity_symbol
Shape with four equal sides and angles
the Learning of Mathematics. 21: 31–36. JSTOR 40248360. Battista, Michael T. (April 1993). "Mathematics in Baseball". The Mathematics Teacher. 86 (4):
Square
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)
German mathematician (born 1992)
German mathematician known for her performance in the International Mathematical Olympiad, where in 2011 she had the single highest (and perfect) score
Lisa_Sauermann
lines, planes, and symplecta. Freudenthal, Hans (1959), "Beziehungen der E7 und E8 zur Oktavenebene. VIII-IX.", Nederlandse Akademie van Wetenschappen
Metasymplectic_space
Sporadic simple group
"The maximal subgroups of the Thompson group", Journal of the London Mathematical Society, Second Series, 39 (1): 79–88, doi:10.1112/jlms/s2-39.1.79, ISSN 0024-6107
Thompson_sporadic_group
SI unit of time
divisions of time could not be measured back then, so such divisions were mathematically derived. The first timekeepers that could count seconds accurately were
Second
Area of mathematics
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general
Catastrophe_theory
Mathematical concept
In mathematics, the seven-dimensional cross product is a bilinear operation on vectors in seven-dimensional Euclidean space. It assigns to any two vectors
Seven-dimensional cross product
Seven-dimensional_cross_product
Group that admits a formal description in terms of reflections
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic
Coxeter_group
In mathematics, a type of algebra
In mathematics, a Lie algebra g {\displaystyle {\mathfrak {g}}} is solvable if its derived series terminates in the zero subalgebra. The derived Lie algebra
Solvable_Lie_algebra
'94 Landsberg, J. M.; Manivel, L. (2006). "The sextonions and E7½". Advances in Mathematics. 201 (1): 143–179. arXiv:math.RT/0402157. doi:10.1016/j.aim
En_(Lie_algebra)
Unsolved problem in number theory
groups over all perfect fields; however, it remains open for anisotropic E6, E7 and E8 groups and trialitarian D4 group over imperfect fields. The conjecture
Serre's_conjecture_II
Sporadic simple group
Robert L. Jr. (1998), Twelve sporadic groups, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, doi:10.1007/978-3-662-03516-0,
McLaughlin_sporadic_group
Type of vector space
"Derived Hecke algebra and cohomology of arithmetic groups". Forum of Mathematics, Pi. 7 e7. arXiv:1608.07234. doi:10.1017/fmp.2019.6. ISSN 2050-5086. Rachel
Hecke_algebra
Concept in mathematics
In mathematics, the special linear Lie algebra of order n {\displaystyle n} over a field F {\displaystyle F} , denoted s l n F {\displaystyle {\mathfrak
Special_linear_Lie_algebra
Theory of subatomic structure
physics, and it has stimulated a number of major developments in pure mathematics. Because string theory potentially provides a unified description of
String_theory
Branch of mathematics
In mathematics, a Lie algebra g {\displaystyle {\mathfrak {g}}} is nilpotent if its lower central series terminates in the zero subalgebra. The lower
Nilpotent_Lie_algebra
Periodic set of points
applications in pure mathematics, particularly in connection to Lie algebras, number theory and group theory. They also arise in applied mathematics in connection
Lattice_(group)
Number in {..., –2, –1, 0, 1, 2, ...}
Mathematical Society. p. 63. the set J of all integers Society, Canadian Mathematical (1960). Canadian Journal of Mathematics. Canadian Mathematical Society
Integer
Polytope in 8-dimensional geometry
group orders. These graphs represent orthographic projections in the E8, E7, E6, and B8, D8, D7, D6, D5, D4, D3, A7, A5 Coxeter planes. The vertex colors
4_21_polytope
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
In mathematics, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. The list of simple
Simple_Lie_group
Group theory theorem
In mathematics, the closed-subgroup theorem (sometimes referred to as Cartan's theorem) is a theorem in the theory of Lie groups. It states that if H
Closed-subgroup_theorem
Concept in Lie algebra mathematics
Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9
Simple_Lie_algebra
Four-dimensional analogue of the cube
Schwartzman, Steven (1994). The Words of Mathematics: An Etymological Dictionary of Mathematical Terms. Mathematical Association of America. p. 219. Elte
Tesseract
English lawyer and mathematician (1869–1962)
were later seen to arise as the roots of the exceptional Lie algebras E6, E7 and E8. A new and more precise definition of the Gosset Series of polytopes
Thorold_Gosset
In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study
Albert_algebra
Matrices named after Élie Cartan
In mathematics, the term Cartan matrix has three meanings. All of these are named after the French mathematician Élie Cartan. Amusingly, the Cartan matrices
Cartan_matrix
Mathematical concept describing isolated singularity of an algebraic surface
original on 2022-05-09. Retrieved 2022-05-09. Reid, Miles, The Du Val singularities An, Dn, E6, E7, E8 (PDF) Burban, Igor, Du Val Singularities (PDF)
Du_Val_singularity
Construct in mathematics
III. The Tate-Šafarevič and Selmer Groups". Proceedings of the London Mathematical Society. s3-13 (1): 768. doi:10.1112/plms/s3-13.1.768-s. Cassels, John
Selmer_group
Thought experiment
In philosophy and mathematics, Newcomb's problem, also known as Newcomb's paradox, is a thought experiment posing a decision problem in which a player
Newcomb's_problem
Theory of strings with supersymmetry
g., John Baez et al.) have speculated that the exceptional Lie groups E6, E7 and E8 having maximum orthogonal subgroups SO(10), SO(12) and SO(16) may be
Superstring_theory
Physics-mathematics connection
Brian C. (2013), Quantum Theory for Mathematicians, Graduate Texts in Mathematics, vol. 267, Springer, Bibcode:2013qtm..book.....H, ISBN 978-1461471158
Particle physics and representation theory
Particle_physics_and_representation_theory
brief chronology of computed numerical values of, or bounds on, the mathematical constant π. For more detailed explanations for some of these calculations
Chronology of computation of pi
Chronology_of_computation_of_pi
Geometric space with seven dimensions
unique polytope from the D7 family, and 321, 231, and 132 polytopes from the E7 family. The 6-sphere or hypersphere in seven-dimensional Euclidean space is
Seven-dimensional_space
Mathematical classification
In mathematics, the ADE classification (originally A-D-E classifications) is a situation where certain kinds of objects are in correspondence with simply
ADE_classification
Form of differential geometry
In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner and developed
Systolic_geometry
Uniform 7-dimensional polytope
polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. It was discovered by Thorold Gosset, published in his 1900 paper. He
3_21_polytope
Class of compact connected topological spaces
of topological groups. For the wrapped loop of wire, see Solenoid. In mathematics, a solenoid is a compact connected topological space (i.e. a continuum)
Solenoid_(mathematics)
Multi-dimensional generalization of triangle
Miller, Jeff, "Simplex", Earliest Known Uses of Some of the Words of Mathematics, retrieved 2018-01-08 Coxeter 1973, pp. 120–124, §7.2. Coxeter 1973,
Simplex
the weight vectors of the 56-dimensional representation of the Lie group E7. Equiangular lines are equivalent to two-graphs. Given a set of equiangular
Equiangular_lines
Extended physical object in string theory
attributes such as charge. Mathematically, branes can be represented within categories, and are studied in pure mathematics for insight into homological
Brane
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
Pictorial representation of symmetry
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double
Dynkin_diagram
Riemannian manifold with SU(n) holonomy
(2022-08-30), "Deep-Learning the Landscape", Machine Learning in Pure Mathematics and Theoretical Physics, World Scientific (Europe), pp. 183–221, doi:10
Calabi–Yau_manifold
Mathematical group
Rubik's Cube group ( G , ⋅ ) {\displaystyle (G,\cdot )} represents the mathematical structure of the Rubik's Cube mechanical puzzle. Each element of the
Rubik's_Cube_group
Mathematical group
In mathematics, the symplectic group is the group of linear transformations that preserve the geometric structure of phase space, the space of position
Symplectic_group
Mathematical concept
In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic
Elliptic_surface
Group of unitary complex matrices with determinant of 1
In mathematics, the special unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the
Special_unitary_group
be made in the E8, E7, E6, D7, D6, D5, D4, D3, A7, A5 Coxeter planes. Ak has [k+1] symmetry, Dk has [2(k-1)] symmetry, and E6, E7, E8 have [12], [18]
E8_polytope
Seven-dimensional geometric object
also list of D7 polytopes for Coxeter plane graphs of these polytopes. The E7 Coxeter group has order 2,903,040. There are 127 forms based on all permutations
Uniform_7-polytope
Sporadic simple group
incorrect statements about the 2-part of the Schur multiplier in the mathematical literature. Burgoyne & Fong (1966) incorrectly claimed that the Schur
Mathieu_group_M22
Lattice in 8-dimensional space with special properties
In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8
E8_lattice
Sporadic simple group
Robert L. Jr. (1998), Twelve sporadic groups, Springer Monographs in Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-3-540-62778-4, MR 1707296
Suzuki_sporadic_group
In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of
List_of_finite_simple_groups
Concept in mathematics
In mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a
Reductive_group
Index of articles associated with the same name
the relation among the four groups is mainly historical rather than mathematical. Janko constructed the first of these groups, J1, in 1965 and predicted
Janko_group
Subgroup of a root system's isometry group
In mathematics, in 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
Weyl_group
In the mathematical theory of linear algebraic groups, a Tits index (or index) is an object used to classify semisimple algebraic groups defined over a
List of irreducible Tits indices
List_of_irreducible_Tits_indices
Symmetry between bosons and fermions
force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry
Supersymmetry
27-dimensional exceptional Jordan algebra it gives a Lie algebra of type E7 of dimension 133. The Kantor–Koecher–Tits construction was used by Kac (1977)
Kantor–Koecher–Tits construction
Kantor–Koecher–Tits_construction
Sporadic simple group
in Corwin, L.; Gelfand, I. M.; Lepowsky, James (eds.), The Gelʹfand Mathematical Seminars, 1990–1992, Boston, MA: Birkhäuser Boston, pp. 137–143, ISBN 978-0-8176-3689-0
Baby_monster_group
Polyhedron with 12 faces
star geometry in mathematics, art and nature". In Emmer, Michele; Abate, Marco (eds.). Imagine Math 6: Between Culture and Mathematics. Springer International
Dodecahedron
Subset of a group that forms a group itself
In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group
Subgroup
Term in mathematics
In the mathematical study of Lie algebras and Lie groups, Satake diagrams are a generalization of Dynkin diagrams that classify involutions of root systems
Satake_diagram
Professionals Organizations Competitions World champions Computers and mathematics Go and mathematics Computer Go Go software Internet Go servers AlphaGo versus Lee
List_of_Go_terms
Finite simple group type not classified as Lie, cyclic or alternating
In the mathematical classification of finite simple groups, there are a number of groups which do not fit into any infinite family. These are called the
Sporadic_group
Hypercomplex number system
In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented
Octonion
Garden Nielsen also appeared in a promotional video for Layman Allen's mathematics game called Equations and in the Seaworld San Antonio Summer Nights 4-D
Leslie_Nielsen_filmography
Transformations induced by a mathematical group
In mathematics, an action of a group G {\displaystyle G} on a set S {\displaystyle S} is, loosely speaking, an operation that takes an element of G {\displaystyle
Group_action
Sporadic simple group
Aschbacher, Michael (1997), 3-transposition groups, Cambridge Tracts in Mathematics, vol. 124, Cambridge University Press, doi:10.1017/CBO9780511759413,
Fischer_group_Fi22
Country in Southern and Western Europe
Hunter-Gatherer Ancestry in the Iberian Peninsula". Current Biology. 29 (7): 1169–1177.e7. doi:10.1016/j.cub.2019.02.006. PMID 30880015. Olalde, Iñigo; Mallick, Swapan;
Spain
Species of cnidarian
Monomeric GFP from Olindias formosa". Cell Chemical Biology. 25 (3): 330–338.e7. doi:10.1016/j.chembiol.2017.12.005. PMID 29290624. "Gamillus at FPbase".
Flower_hat_jelly
endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra
List_of_group_theory_topics
Type of group in mathematics
In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension
Orthogonal_group
Comparison of a wide range of temperatures
Hadron Collider". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 370 (1961): 917–932. arXiv:1109.4291
Orders of magnitude (temperature)
Orders_of_magnitude_(temperature)
Chinese electric car brand by BYD Auto
"Fangchengbao" translates to "formula leopard," and the logo reflects this mathematical concept. On August 16, 2023, Fangchengbao released its first model, the
Fangchengbao
Plane figure bounded by line segments
Teaching Mathematics. 2015 (18): 23–28. Coxeter (3rd Ed 1973) Günter Ziegler (1995). "Lectures on Polytopes". Springer Graduate Texts in Mathematics, ISBN 978-0-387-94365-7
Polygon
2007 book by Ian Stewart
octonions), the exceptional simple Lie algebras detected by Killing (G2, F4, E6, E7, and E8), and symmetries occurring in string theory are explored. Chapter
Why_Beauty_Is_Truth
Type of two-dimensional barcode
77 72 E7 76 96 B6 97 06 56 46 96 12 E6 F7 26 70] Using the procedure for Reed-Solomon systematic encoding, the 7 EC bytes obtained (E1 through E7, as shown
QR_code
Concept in algebraic geometry
In mathematics, a del Pezzo surface or Fano surface is a two-dimensional Fano variety, in other words a non-singular projective algebraic surface with
Del_Pezzo_surface
Symmetric bilinear form in mathematics
In mathematics, the Killing form, named after Wilhelm Killing, is a symmetric bilinear form that plays a basic role in the theories of Lie groups and
Killing_form
Natural number
positive integers. 126 is the number of root vectors of simple Lie group E7. 126 = 6 × 21, making it a Friedman number. 126 is the seventh magic number
126_(number)
Framework of superstring theory
Physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality. Witten's conjecture was
M-theory
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E7 MATHEMATICS
E7 MATHEMATICS
E7 MATHEMATICS
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E7 MATHEMATICS
E7 MATHEMATICS
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E7 MATHEMATICS
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