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...

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...

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...

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...

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...

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

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...

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...

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

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...

unipotent representation of a reductive group is a representation that has some similarities with unipotent conjugacy classes of groups. Informally, Langlands...

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...

linearly reductive groups acting on regular rings are Cohen–Macaulay. In other words, if V is a rational representation of a linearly reductive group G over...

subgroup of a reductive algebraic group over a nonarchimedean local field that is analogous to a Borel subgroup of an algebraic group. A parahoric subgroup...

complex reductive group. If the complex vector space is given a norm that is invariant under a maximal compact subgroup of the reductive group, then the...

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations...

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...

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...

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...

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...

specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently...

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...

similar result holds for any PSL(2, q2), q odd. Let G now be a connected reductive group over an algebraically closed field. Then any two Borel subgroups are...

mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted Sp(2n, F) and Sp(n) for...

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...

finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called...

mathematics, the Moy–Prasad filtration is a family of filtrations of p-adic reductive groups and their Lie algebras, named after Allen Moy and Gopal Prasad. The...

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...