reductive algebra
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Reductive group — In mathematics, a reductive group is an algebraic group G such that the unipotent radical of the identity component of G is trivial. Any semisimple algebraic group and any algebraic torus is reductive, as is any general linear group.The name… … Wikipedia
Reductive dual pair — In the mathematical field of representation theory, a reductive dual pair is a pair of subgroups (G,G ′) of the isometry group Sp(W) of a symplectic vector space W, such that G is the centralizer of G ′ in Sp(W) and vice versa, and these groups… … 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
Compact Lie algebra — Lie groups … Wikipedia
Semisimple Lie algebra — In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non abelian Lie algebras mathfrak g whose only ideals are {0} and mathfrak g itself. It is called reductive if it is the sum of a semisimple and an… … Wikipedia
Super-Poincare algebra — In theoretical physics, a super Poincaré algebra is an extension of the Poincaré algebra to incorporate supersymmetry, a relation between bosons and fermions. They are examples of supersymmetry algebras, and hence are Lie superalgebra. Thus a… … Wikipedia
Nilradical of a Lie algebra — In algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible. The nilradical of a finite dimensional Lie algebra is its maximal nilpotent ideal, which exists because the sum of any two nilpotent ideals is… … Wikipedia
Gelfand pair — In mathematics, the expression Gelfand pair refers to a pair ( G , K ) consisting of a group G and a subgroup K that satisfies a certain property on restricted representations.When G is a finite group the simplest definition is, roughly speaking … Wikipedia
Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) … Wikipedia
Representation theory of SL2(R) — In mathematics, the main results concerning irreducible unitary representations of the Lie group SL2(R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish Chandra (1952). Structure of the complexified Lie algebra We choose a… … Wikipedia
Simple Lie group — Lie groups … Wikipedia
