reductive group

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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 amination — (also known as reductive alkylation) is a form of amination that involves the conversion of a carbonyl group to an amine via an intermediate imine. The carbonyl group is most commonly a ketone or an aldehyde. Contents 1 …   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

• Group of Lie type — In mathematics, a group of Lie type G(k) is a (not necessarily finite) group of rational points of a reductive linear algebraic group G with values in the field k. Finite groups of Lie type form the bulk of nonabelian finite simple groups.… …   Wikipedia

• Langlands group — In representation theory, a branch of mathematics, the Langlands (dual) group L G (also called L group) is a group associated to a reductive group G over a field k that controls the representation theory of G . It is an extension of the absolute… …   Wikipedia

• Dual group — In mathematics, the dual group may be: The Pontryagin dual of a locally compact abelian group The Langlands dual of a reductive algebraic group The Deligne Lusztig dual of a reductive group over a finite field. This disambiguation page lists… …   Wikipedia

• Outer automorphism group — In mathematics, the outer automorphism group of a group G is the quotient Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually …   Wikipedia

• Representation of a Lie group — In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the… …   Wikipedia

• Simple Lie group — Lie groups …   Wikipedia

• Metaplectic group — In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the… …   Wikipedia

• Gorani (ethnic group) — Infobox Ethnic group group=Goran poptime = 84,000 popplace = region1 = flagcountry|Serbia: 18 villages1 region2 = flagcountry|Albania: 11 villages region3 = flagcountry|Macedonia|name=Republic of Macedonia: 2 villages langs = Albanian / Shqip,… …   Wikipedia