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Action of a semigroup on a set
theoretical computer science, an action or act of a semigroup on a set is a rule which associates to each element of the semigroup a transformation of the set
Semigroup_action
Algebraic structure
appears in the theory of one-parameter operator semigroups: see C0-semigroup. The binary operation of a semigroup is most often denoted multiplicatively: x
Semigroup
the semigroup analogue of a permutation group. A transformation semigroup of a set has a tautological semigroup action on that set. Such actions are characterized
Transformation_semigroup
Topics referred to by the same term
Continuous group action Semigroup action Ring action Action (firearms), the mechanism that manipulates cartridges and/or seals the breech Action! (programming
Action
Transformations induced by a mathematical group
maps and equivalence relations however. See semigroup action. Instead of actions on sets, we can define actions of groups and monoids on objects of an arbitrary
Group_action
Mathematical model of computation
automaton SCXML Semiautomaton Semigroup action Sequential logic State diagram Synchronizing word Transformation semigroup Transition system Tree automaton
Finite-state_machine
J. William (1978). "Orbit structure of the Mobius transformation semigroup action on H-infinity (broadband matching)". Adv. Math. Suppl. Stud. 3: 129–197
H-infinity methods in control theory
H-infinity_methods_in_control_theory
Approach to the study of finite semigroups and automata
finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and
Krohn–Rhodes_theory
State machine that may have infinite states
relation Ternary relation Transition monoid Transformation monoid Semigroup action Simulation preorder Bisimulation Operational semantics Kripke structure
Transition_system
Preston (1967) semigroup actions are called "operands". In category theory, semiautomata essentially are functors. A transformation semigroup or transformation
Semiautomaton
Structure in group theory (in mathematics)
In group theory, an inverse semigroup (occasionally called an inversion semigroup) S is a semigroup in which every element x in S has a unique inverse
Inverse_semigroup
Topics referred to by the same term
set, a two-dimensional fractal shape A monoid acting on a set; see Semigroup action This disambiguation page lists articles associated with the title M-set
M-set
direct product of a right zero semigroup and a group, while a right abelian group is the direct product of a right zero semigroup and an abelian group. Left
Right_group
Algebraic structure with an associative operation and an identity element
with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of
Monoid
Characterization of how many integers are prime
prime number theorem and disjointness of additive and multiplicative semigroup actions. Duke Mathematical Journal, 171(15), 3133-3200. Avigad, Jeremy; Donnelly
Prime_number_theorem
Special types of subgroups encountered in group theory
apply to semigroups. In ring theory, the centralizer of a subset of a ring is defined with respect to the multiplication of the ring (a semigroup operation)
Centralizer_and_normalizer
Representation theory of the symplectic group
representation leads to a semigroup of contraction operators, introduced as the oscillator semigroup by Roger Howe in 1988. The semigroup had previously been
Oscillator_representation
maximal cone. A similar decomposition already occurs in the semigroup. The oscillator semigroup of Roger Howe concerns the special case of this theory for
Invariant_convex_cone
Branch of mathematics that studies algebraic structures
lemma Semigroup Subsemigroup Free semigroup Green's relations Inverse semigroup (or inversion semigroup, cf. [1]) Krohn–Rhodes theory Semigroup algebra
List of abstract algebra topics
List_of_abstract_algebra_topics
Semigroup action
of representation theory, a representation of a Lie superalgebra is an action of Lie superalgebra L on a Z2-graded vector space V, such that if A and
Representation of a Lie superalgebra
Representation_of_a_Lie_superalgebra
Theorem about the distribution of primes
prime number theorem and disjointness of additive and multiplicative semigroup actions", Duke Mathematical Journal, 171 (15): 3133–3200, arXiv:2002.03498
Erdős–Delange_theorem
Theorem in group theory
similar to the universal embedding theorem, but for semigroups. A semigroup S is a divisor of a semigroup T if it is the image of a subsemigroup of T under
Universal_embedding_theorem
Mathematical conjecture
their conjecture was proven in 2007 by Avraham Trahtman. A transformation semigroup is synchronizing if it contains an element of rank 1, that is, an element
Synchronizing_word
Differential operator in mathematics
is a strongly continuous contraction semigroup whose generator is the Laplacian; more generally, the heat semigroup acts contractively on Lp for 1 ≤ p ≤
Laplace_operator
Topics referred to by the same term
semi-algebraic systems in computer algebra Regular semigroup, related to the previous sense *-regular semigroup Borel regular measure Cauchy-regular function
Regular
Generalization of vector spaces from fields to rings
K[x]-module M is a K-module with an additional action of x on M by a group homomorphism that commutes with the action of K on M. In other words, a K[x]-module
Module_(mathematics)
Generalized function whose value is zero everywhere except at zero
easy to see that this generates a semigroup in some sense—it is not absolutely integrable and so cannot define a semigroup in the above strong sense. Many
Dirac_delta_function
Topic in group theory
notion generalizes to semigroups and, as such, is a central construction in the Krohn–Rhodes structure theory of finite semigroups. Let A {\displaystyle
Wreath_product
Motion of particles in a fluid
boundary condition. The mathematical setting for this problem can be the semigroup approach. To use this tool, we introduce the unbounded operator ΔD defined
Flow_(mathematics)
Concept in mathematics regarding sets operating on groups
as a group G = ( G , ⋅ ) {\displaystyle G=(G,\cdot )} together with an action of a set Ω {\displaystyle \Omega } on G {\displaystyle G} : Ω × G → G :
Group_with_operators
Group of 𝑛 × 𝑛 invertible matrices
monoid, but occasionally also full linear semigroup, general linear monoid etc. It is actually a regular semigroup. The infinite general linear group or stable
General_linear_group
Category where every morphism is invertible; generalization of a group
manifolds. Heinrich Brandt (1927) introduced groupoids implicitly via Brandt semigroups. A groupoid can be viewed as an algebraic structure consisting of a set
Groupoid
American mathematician
(1997). Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions. Springer. pp. 133–134. ISBN 9780306455506. "In Memoriam: Robert Ellis"
Robert_Ellis_(mathematician)
Algebraic structure with only one element
(mathematics) Examples of vector spaces Field with one element Empty semigroup Zero element List of zero terms David Sharpe (1987). Rings and factorization
Zero_object_(algebra)
Lie group homomorphism from the real numbers
real line. Exponential map (Lie theory) Integral curve One-parameter semigroup Noether's theorem The Wikibook Abstract Algebra has a page on the topic
One-parameter_group
String rewriting system
introduced this notion hoping to solve the word problem for finitely presented semigroups. Only in 1947 was the problem shown to be undecidable— this result was
Semi-Thue_system
isometries (and projections) can be defined in the more abstract setting of a semigroup with involution; the definition coincides with the one herein. In finite-dimensional
Partial_isometry
Lie group of complex numbers of unit modulus; topologically a circle
then the orbit is dense, and in fact equidistributed. Similarly, the semigroup of translations R a , R a 2 , … {\displaystyle R_{a},R_{a}^{2},\dots }
Circle_group
representation R. Exel (1998) Exel, Ruy (1998). "Partial Actions of Groups and Actions of Inverse Semigroups". Proceedings of the American Mathematical Society
Partial_group_algebra
German mathematician (1886–1954)
forms); the theory is now considered by means of Brandt module. Brandt semigroup H.-J. Hoehnke and M.-A. Knus (2004) A Tribute to (the work of) Heinrich
Heinrich_Brandt
In mathematics, element with a multiplicative inverse
relation ~ can be viewed as any one of Green's semigroup relations specialized to the multiplicative semigroup of a commutative ring R. S-units Localization
Unit_(ring_theory)
Commutative group (mathematics)
Algebraic structures Group-like Group Semigroup / Monoid Rack and quandle Quasigroup and loop Abelian group Magma Lie group Group theory Ring-like Ring
Abelian_group
Subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics
initial arbitrary mixed state as well. This formulation makes use of the semigroup approach. The Lindblad decohering term determines when the dynamics of
Decoherence-free_subspaces
Property of measure-preserving dynamical systems
with invariant measures taken with respect to the corresponding flow or semigroup. The transformation T {\displaystyle T} is said to be uniquely ergodic
Ergodicity
Pakistani mathematician
who has made numerous contributions in the field of Group theory and Semigroup. He has been vice-chancellor of The Islamia University Bahawalpur from
Qaiser_Mushtaq
Set with associative invertible operation
inverse) is removed. For a structure with a looser definition (like a semigroup) one may have, for example, that a left identity is not necessarily a
Group_(mathematics)
Subset of real numbers that are greater than zero
structure of a multiplicative topological group or of an additive topological semigroup. For a given positive real number x , {\displaystyle x,} the sequence
Positive_real_numbers
course titles. Abstract analytic number theory The study of arithmetic semigroups as a means to extend notions from classical analytic number theory. Abstract
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Schreier vector Strong generating set Symmetric group Symmetric inverse semigroup Weak order of permutations Wreath product Young symmetrizer Zassenhaus
List_of_permutation_topics
(Russian: Свердловская тетрадь) is a collection of unsolved problems in semigroup theory, first published in 1965 and updated every 2 to 4 years since.
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematical model of the time dependence of a point in space
measure space M {\displaystyle {\mathfrak {M}}} , Φ is also the action of a semigroup T as the general case. Here the Measure space M {\displaystyle {\mathfrak
Dynamical_system
Branch of mathematics that studies dynamical systems
result also extends to the case of strongly continuous one-parameter semigroup of contractive operators on a reflexive space. Remark: Some intuition
Ergodic_theory
Aspect of group theory in mathematics
generate a free semigroup. Such versions are available both in the general context of a group action on a set, and for specific types of actions, e.g. in the
Ping-pong_lemma
Decomposition of an algebraic structure
only depends on A and is called the length of A. Krohn–Rhodes theory, a semigroup analogue Schreier refinement theorem, any two subnormal series have equivalent
Composition_series
Representation of groups by permutations
original theorem. Wagner–Preston theorem is the analogue for inverse semigroups. Birkhoff's representation theorem, a similar result in order theory Frucht's
Cayley's_theorem
Partial differential equation describing the evolution of temperature in a region
dissipative, thus by the spectral theorem it generates a one-parameter semigroup. In the special cases of propagation of heat in an isotropic and homogeneous
Heat_equation
Vector space equipped with a bilinear product
it isn't, then the multiplication is still completely determined by its action on a set that spans A; however, the structure constants can't be specified
Algebra_over_a_field
Sets with binary operations analogous to the Reidemeister moves used on knot diagrams
say that these left and right actions are inverses of each other. Using this, we can eliminate either one of these actions from the definition of rack.
Racks_and_quandles
Subset of a group that forms a group itself
of H. The same definitions apply more generally when G is an arbitrary semigroup, but this article will only deal with subgroups of groups. Suppose that
Subgroup
Subgroup invariant under conjugation
Paranormal subgroup Polynormal subgroup C-normal subgroup Ideal (ring theory) Semigroup ideal In other language: det {\displaystyle \det } is a homomorphism from
Normal_subgroup
Mathematical term in group theory
Mathematicae, vol. 219 (2020), no.3, pp 1069–1155. Mahlon M. Day. Amenable semigroups. Illinois Journal of Mathematics, vol. 1 (1957), pp. 509–544. Volodymyr
Grigorchuk_group
Generalization of associativity properties
\tau _{i}} . The algebras over the associative operad are precisely the semigroups: sets together with a single binary associative operation. The k-linear
Operad
from a collection of subsets of a set X {\displaystyle X} to an abelian semigroup. For example, Lebesgue measure is a valuation on finite unions of convex
Valuation_(geometry)
Type of vector space in math
states the following: If Ut is a (strongly continuous) one-parameter semigroup of unitary operators on a Hilbert space H, and P is the orthogonal projection
Hilbert_space
science, a splicing language is a formal language which formalizes the action of gene splicing in molecular biology. Splicing languages have a variety
Splicing_language
Type of group in abstract algebra
group Symmetry in quantum mechanics § Exchange symmetry Symmetric inverse semigroup Symmetric power Jacobson 2009, p. 31 Jacobson 2009, p. 32 Theorem 1.1
Symmetric_group
Field of mathematics
a continuous transformation, a continuous flow, or more generally, a semigroup of continuous transformations of that space. The origins of topological
Topological_dynamics
Group that is a topological space with continuous group operations
descriptions of redirect targets Topological module Topological ring Topological semigroup Topological vector space – Vector space with a notion of nearness i.e
Topological_group
Algebraic structure with addition and multiplication
transitive actions of the group and whose addition is the disjoint union of the action. Expressing an action in terms of the basis is decomposing an action into
Ring_(mathematics)
Orientation-preserving mapping class group of the torus
Pell's equation. In both cases, the numbers can be arranged to form a semigroup subset of the modular group. The modular group can be shown to be generated
Modular_group
Group in group theory and physics
{\mathcal {L}}=-\sum _{j=1}^{n}(X_{j}^{2}+Y_{j}^{2}),} the corresponding heat semigroup is generated by − 1 2 L {\displaystyle -{\frac {1}{2}}{\mathcal {L}}}
Heisenberg_group
Euclidean Wightman distributions
has to be positive semidefinite. (OS4) Ergodicity. The time translation semigroup acts ergodically on the measure space ( D ′ ( R d ) , d μ ) {\displaystyle
Schwinger_function
Algebraic structure
3 + 1 , {\displaystyle X^{6}+X^{3}+1,} and are all conjugate under the action of the Galois group. The twelve primitive 21 {\displaystyle 21} st roots
Finite_field
Relationship between two functors abstracting many common constructions
ring to the underlying rng. Adjoining an identity to a semigroup. Similarly, given a semigroup S, we can add an identity element and obtain a monoid by
Adjoint_functors
Israeli mathematician
(2011). "Stationary measures and equidistribution for orbits of nonabelian semigroups on the torus". Journal of the American Mathematical Society. 24: 231–280
Shahar_Mozes
Class of transformations that quantum systems and processes can undergo
completely-positive maps should be considered as well. Quantum dynamical semigroup Superoperator Sudarshan, E. C. G.; Mathews, P. M.; Rau, Jayaseetha (1961)
Quantum_operation
Mathematical theorem
Stone's theorem on one-parameter unitary groups Hille–Yosida theorem C0-semigroup [xn, p] = i ℏ nxn − 1, hence 2‖p‖ ‖x‖n ≥ n ℏ ‖x‖n − 1, so that, ∀n: 2‖p‖ ‖x‖
Stone–von_Neumann_theorem
Group of symmetries of an n-dimensional hypercube
Conference on Geometric and Combinatorial Methods in Group Theory and Semigroup Theory (Lincoln, NE, 2000), Internat. J. Algebra Comput., 12 (1–2): 85–97
Hyperoctahedral_group
Study of computable functions and Turing degrees
and Post published independent papers showing that the word problem for semigroups cannot be effectively decided. Extending this result, Pyotr Novikov and
Computability_theory
Theoretical object in mathematics
related number-theoretic transform (Z/nZ‑valued). Arithmetic derivative Semigroup with one element "un" is French for "one", and fun is a playful English
Field_with_one_element
Chinese-American mathematician (born 1949)
Zbl 1079.60005. Wang, Feng-Yu (2005). Functional inequalities, Markov semigroups and spectral theory. Beijing/New York: Science Press. doi:10.1016/B978-0-08-044942-5
Shing-Tung_Yau
Sapir – Russian-American mathematician working in geometric group theory, semigroup theory and combinatorial algebra, Centennial Professor of Mathematics
List of Vanderbilt University people
List_of_Vanderbilt_University_people
Magma Module Monoid Monoid ring Quandle Quasigroup Quantum group Ring Semigroup Vector space Affine representation Character theory Great orthogonality
List_of_group_theory_topics
Mathematical object that generalizes the standard notions of sets and functions
morphism is an isomorphism. Groupoids are generalizations of groups, group actions and equivalence relations. From the point of view of category theory, a
Category_(mathematics)
Algebraic structure in linear algebra
precisely, an affine space is a set with a free transitive vector space action. In particular, a vector space is an affine space over itself, by the map
Vector_space
American mathematician
assumption of dynamics is that one has a phase space and some group or semigroup of self-maps of that space that play the role of describing time evolution
Daniel_Rudolph
Property of some mathematical functions
subsets of an amenable group, and further, of a cancellative left-amenable semigroup. Theorem:—For every measurable subadditive function f : ( 0 , ∞ ) → R
Subadditivity
1969 non-fiction book by G. Spencer-Brown
theory.) To see this, note that the primary algebra is a commutative: Semigroup because primary algebra juxtaposition commutes and associates; Monoid
Laws_of_Form
Result of repeatedly applying a mathematical function
the full orbit: the monoid of the Picard sequence (cf. transformation semigroup) has generalized to a full continuous group. This method (perturbative
Iterated_function
American mathematician (born 1931)
114685, 37. Charalambous, Nelia; Gross, Leonard: The Yang-Mills heat semigroup on three-manifolds with boundary. Comm. Math. Phys. 317 (2013), no. 3
Leonard_Gross
Locally compact topological group with an invariant averaging operation
Helv. 56: 581–598. doi:10.1007/bf02566228. Day, M. M. (1949). "Means on semigroups and groups". Bulletin of the American Mathematical Society. 55 (11): 1054–1055
Amenable_group
Objective collapse theory in quantum mechanics
S2CID 13923422. Lindblad, G. (1976). "On the generators of quantum dynamical semigroups". Communications in Mathematical Physics. 48 (2): 119–130. Bibcode:1976CMaPh
Ghirardi–Rimini–Weber_theory
British-Australian mathematician
George (2020). "A graph-theoretic description of scale-multiplicative semigroups of automorphisms". Israel Journal of Mathematics. 237: 221–265. arXiv:1710
Jacqui_Ramagge
Berg, Christian; Christensen, Paul; Ressel (1984). Harmonic Analysis on Semigroups. Graduate Texts in Mathematics. Vol. 100. Springer Verlag. Constantinescu
Positive-definite function on a group
Positive-definite_function_on_a_group
American mathematician
Continuous Symmetry, American Mathematical Monthly 118:565–8. Oscillator semigroup Li, Yeping; Lewis, W. James; Madden, James (Eds.) (2018). Mathematics
Roger_Evans_Howe
Branch of algebra
polynomial ring k [ V ] {\displaystyle k[V]} that are invariant under the action of a finite group (or more generally reductive) G on V. The main example
Ring_theory
ISBN 978-0-521-84425-3. Zbl 1188.68177. Robert, Leonel (3 September 2013). "The Cuntz semigroup of some spaces of dimension at most two". arXiv:0711.4396 [math.OA]. Lightstone
Extended_natural_numbers
Ring that is also a vector space or a module
ring R. Then the algebra A is a right module over Ae := Aop ⊗R A with the action x ⋅ (a ⊗ b) = axb. Then, by definition, A is said to separable if the multiplication
Associative_algebra
Theorem about projections of coadjoint orbits of a connected compact Lie group
Karl Heinrich; Lawson, Jimmie D. (1989), Lie groups, convex cones, and semigroups, Oxford Mathematical Monographs, Oxford University Press, ISBN 978-0-19-853569-0
Kostant's_convexity_theorem
arXiv:math.CO/0001078. Arveson, William (2003), Noncommutative dynamics and E-semigroups, New York: Springer, ISBN 0-387-00151-4. Tsirelson, Boris (2003), "Non-isomorphic
List of probabilistic proofs of non-probabilistic theorems
List_of_probabilistic_proofs_of_non-probabilistic_theorems
SEMIGROUP ACTION
SEMIGROUP ACTION
Girl/Female
Hindu
Famous action
Boy/Male
Hindu
Deed, Action
Girl/Female
Tamil
Satkrithi | ஸதà¯à®•à¯à®°à¯€à®¤à¯€
Good action
Satkrithi | ஸதà¯à®•à¯à®°à¯€à®¤à¯€
Girl/Female
Muslim
Determined action
Girl/Female
Tamil
Action
Girl/Female
Tamil
Kirthika | கிரà¯à®¤à¯€à®•à®¾, கீரà¯à®¤à¯€à®•à®¾Â
Famous action
Kirthika | கிரà¯à®¤à¯€à®•à®¾, கீரà¯à®¤à¯€à®•à®¾Â
Boy/Male
Hindu
Action
Boy/Male
Tamil
Action
Boy/Male
Muslim
Deed, Action
Girl/Female
Indian
Determined action
Girl/Female
Hindu
Action, A work of art
Boy/Male
Tamil
Deed, Action
Boy/Male
Sikh
One whose actions are gem-like, Friendly gem
Girl/Female
Tamil
Action, A work of art
Girl/Female
Hindu
Action, A work of art
Girl/Female
Tamil
Action, A work of art
Boy/Male
Tamil
Karmendra | கரà¯à®®à¯‡à®¨à¯à®¤à¯à®°
God of action
Karmendra | கரà¯à®®à¯‡à®¨à¯à®¤à¯à®°
Boy/Male
Hindu
Deed, Action
Girl/Female
Tamil
Kirtika | கிரà¯à®¤à¯€à®•à®¾, கீரà¯à®¤à¯€à®•à®¾Â
Famous action
Kirtika | கிரà¯à®¤à¯€à®•à®¾, கீரà¯à®¤à¯€à®•à®¾Â
Girl/Female
Hindu
Famous action
SEMIGROUP ACTION
SEMIGROUP ACTION
Girl/Female
American, Australian, British, Chinese, Christian, Danish, Dutch, English, Finnish, French, German, Gujarati, Hindu, Indian, Japanese, Kannada, Netherlands, Polish, Romanian, Sindhi, Spanish, Swedish, Swiss, Tamil, Teutonic
Advice; Decision; Decision and Protector; Wise Guardian; Counsel Protection; Might Protector
Boy/Male
Muslim
Paradise, Heaven, Garden
Boy/Male
Sikh
Gurus splendor, His banishment, The change of pilgrimage
Girl/Female
Irish Hebrew
Bitter.
Girl/Female
Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sindhi, Tamil, Telugu
Light; A Flame
Girl/Female
Indian
Wife of Brihaspati
Girl/Female
Gujarati, Hindu, Indian, Italian, Kannada, Tamil, Telugu
Money
Girl/Female
Indian, Sanskrit
Active; Strong
Boy/Male
Tamil
Trishiv | தà¯à®°à¯€à®·à¯€à®µÂ
Boy/Male
Indian, Sanskrit
Stable
SEMIGROUP ACTION
SEMIGROUP ACTION
SEMIGROUP ACTION
SEMIGROUP ACTION
SEMIGROUP ACTION
n.
a state of opposition or contest; an act of opposition; an inimical contest, act, or action; enmity; hostility.
n.
An engagement between troops in war, whether on land or water; a battle; a fight; as, a general action, a partial action.
n.
Any one of the active processes going on in an organism; the performance of a function; as, the action of the heart, the muscles, or the gastric juice.
n.
Action by, or originating in, one's self or itself.
n.
Conduct; course of action; behavior.
v. t.
To put in motion or action; to arouse; to excite.
n.
A frequented track; habitual place of action; sphere; as, the walk of the historian.
v. t.
To excite; to rouse; to move to action; to awaken.
n.
A right of action; as, the law gives an action for every claim.
n.
A process or condition of acting or moving, as opposed to rest; the doing of something; exertion of power or force, as when one body acts on another; the effect of power exerted on one body by another; agency; activity; operation; as, the action of heat; a man of action.
n.
Movement; as, the horse has a spirited action.
v. i.
To be in action or motion; to move; to get along; to progress; to stir.
adv.
In an actionable manner.
n.
Alt. of Actionist
n.
The manner or action of a wag; mischievous merriment; sportive trick or gayety; good-humored sarcasm; pleasantry; jocularity; as, the waggery of a schoolboy.
a.
That may be the subject of an action or suit at law; as, to call a man a thief is actionable.
n.
The science which treats of phenomena due to plutonic action, as in volcanoes, hot springs, etc.
a.
Void of action.
n.
The revival of an action.
n.
Effective motion; also, mechanism; as, the breech action of a gun.