field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some...

require reductive groups to be connected.) A semisimple group is reductive. A group G over an arbitrary field k is called semisimple or reductive if G k...

reductive groups, but over non-perfect fields Jacques Tits found some examples of pseudo-reductive groups that are not reductive. A pseudo-reductive k-group...

Reductive amination (also known as reductive alkylation) is a form of amination that converts a carbonyl group to an amine via an intermediate imine. The...

algebraic group is (essentially) a semidirect product of a unipotent group (its unipotent radical) with a reductive group. In turn, a reductive group is decomposed...

the unipotent radical, it serves to define reductive groups. Reductive group Unipotent group "Radical of a group", Encyclopaedia of Mathematics v t e...

Reductive desulfonylation reactions are chemical reactions leading to the removal of a sulfonyl group from organic compounds. As the sulfonyl functional...

for one semisimple (or reductive) Lie group, can be done for all. Therefore, once the role of some low-dimensional Lie groups such as GL(2) in the theory...

connected reductive algebraic group over the algebraically closed field K, then its Langlands dual group LG is the complex connected reductive group whose...

constructing representations of a reductive group from representations of its parabolic subgroups. If G is a reductive algebraic group and P = M A N {\displaystyle...

ISBN 978-3-540-07686-5, MR 0444786 Haboush, W. J. (1975), "Reductive groups are geometrically reductive", Annals of Mathematics, 102 (1): 67–83, doi:10.2307/1970974...

are (G, K), where G is a reductive Lie group and K is a maximal compact subgroup. When G is a locally compact topological group and K is a compact subgroup...

a quasi-split group over a field is a reductive group with a Borel subgroup defined over the field. Simply connected quasi-split groups over a field correspond...

finite groups, or just the sporadic groups. A simple group is a group G that does not have any normal subgroups except for the trivial group and G itself...

The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group; it has...

polynomials, an analogue of Kazhdan–Lusztig polynomials introduced for reductive groups in general by George Lusztig and David Kazhdan (1983). The values at...

in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear...

collection of (isomorphism classes of) irreducible representations of a reductive group over a local field, that are L-indistinguishable, meaning they have...

mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest...

relates orbital integrals on a reductive group over a local field to stable orbital integrals on its endoscopic groups.[clarification needed] It was conjectured...

In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces...

nitro group was one of the first functional groups to be reduced. Alkyl and aryl nitro compounds behave differently. Most useful is the reduction of aryl...

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...

representation of a reductive algebraic group such as GL2 over a finite or local or global field on a space of functions on the group. It is named after...

general group. Lie groups appear in symmetry groups in geometry, and also in the Standard Model of particle physics. The Poincaré group is a Lie group consisting...

In mathematics, the general linear group of degree n {\displaystyle n} is the set of n × n {\displaystyle n\times n} invertible matrices, together with...

identifies the Hecke algebra of a reductive group over a local field with a ring of invariants of the Weyl group. The geometric Satake equivalence is...

In geometry and group theory, a lattice in the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} is an infinite set of points in this space with...