Quantum group — In mathematics and theoretical physics, quantum groups are certain noncommutative algebras that first appeared in the theory of quantum integrable systems, and which were then formalized by Vladimir Drinfel d and Michio Jimbo. There is no single … Wikipedia
Affine Lie algebra — In mathematics, an affine Lie algebra is an infinite dimensional Lie algebra that is constructed in a canonical fashion out of a finite dimensional simple Lie algebra. It is a Kac–Moody algebra whose generalized Cartan matrix is positive semi… … Wikipedia
Affine Hecke algebra — DefinitionLet V be a Euclidean space of a finite dimension and Sigma an affine root system on V. An affine Hecke algebra is a certain associative algebra that deforms the group algebra mathbb{C} [W] of the Weyl group W of Sigma (the affine Weyl… … Wikipedia
Coxeter group — In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry … Wikipedia
Lorentz group — Group theory Group theory … Wikipedia
Lie group — Lie groups … Wikipedia
Poincaré group — In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime. It is a 10 dimensional noncompact Lie group. The abelian group of translations is a normal subgroup while the Lorentz… … Wikipedia
Representation theory of the Galilean group — In nonrelativistic quantum mechanics, an account can be given of the existence of mass and spin as follows:The spacetime symmetry group of nonrelativistic quantum mechanics is the Galilean group. In 3+1 dimensions, this is the subgroup of the… … Wikipedia
Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 … Wikipedia
Hecke algebra — is the common name of several related types of associative rings in algebra and representation theory. The most familiar of these is the Hecke algebra of a Coxeter group , also known as Iwahori Hecke algebra, which is a one parameter deformation… … Wikipedia
