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...

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...

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...

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

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...

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...

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...

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, having...

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...

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...

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...

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...

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

In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it...

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...

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...

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...

A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that...

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...

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...

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...

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 abstract algebra, a cyclic group or monogenous group is a group, denoted C n {\displaystyle C_{n}} (also frequently Z n {\displaystyle \mathbb {Z} _{n}}...

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 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...