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Longer titles found: Linear algebraic group (view), Adelic algebraic group (view), Radical of an algebraic group (view), Approximation in algebraic groups (view), Differential algebraic group (view), Special group (algebraic group theory) (view), Distribution on a linear algebraic group (view), Thin group (algebraic group theory) (view)

searching for Algebraic group 74 found (371 total)

alternate case: algebraic group

Langlands dual group (936 words) [view diff] exact match in snippet view article find links to article

theory, a branch of mathematics, the Langlands dual LG of a reductive algebraic group G (also called the L-group of G) is a group that controls the representation

Lie algebra bundle (540 words) [view diff] exact match in snippet view article find links to article

was proved by proving that the real orbit of a real point under an algebraic group is open in the real part of its complex orbit. Suppose the base space

Williams's p + 1 algorithm (819 words) [view diff] no match in snippet view article find links to article

algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by Hugh C. Williams in 1982

Ree group (2,067 words) [view diff] exact match in snippet view article find links to article

points of a connected reductive algebraic group defined over a finite field; in other words, there is no "Ree algebraic group" related to the Ree groups in

Iwahori subgroup (800 words) [view diff] exact match in snippet view article find links to article

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

Fixed-point subring (603 words) [view diff] exact match in snippet view article find links to article

x_{n}]^{\operatorname {S} _{n}}} is the ring of symmetric polynomials. If a reductive algebraic group G acts on R, then the fundamental theorem of invariant theory describes

Ernő Rubik (2,069 words) [view diff] exact match in snippet view article find links to article

solve the problem of the cube. It proved a useful tool for teaching algebraic group theory, and in late 1977 Konsumex, Hungary's state trading company

Serre's conjecture II (algebra) (408 words) [view diff] exact match in snippet view article

statement regarding the Galois cohomology of a simply connected semisimple algebraic group. Namely, he conjectured that if G is such a group over a perfect field

Pollard's p − 1 algorithm (1,234 words) [view diff] no match in snippet view article find links to article

integers with specific types of factors; it is the simplest example of an algebraic-group factorisation algorithm. The factors it finds are ones for which the

Haboush's theorem (1,094 words) [view diff] exact match in snippet view article find links to article

referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K, and for any linear representation ρ of G on a K-vector

Parabolic induction (386 words) [view diff] exact match in snippet view article find links to article

from representations of its parabolic subgroups. If G is a reductive algebraic group and P=MAN{\displaystyle P=MAN} is the Langlands decomposition of a

Reynolds operator (986 words) [view diff] exact match in snippet view article find links to article

theory the average is often taken over a compact group or reductive algebraic group acting on a commutative algebra, such as a ring of polynomials. Reynolds

Birkhoff factorization (252 words) [view diff] exact match in snippet view article find links to article

where the general linear group is replaced by some other reductive algebraic group, due to Alexander Grothendieck (1957). Birkhoff factorization implies

Jantzen filtration (293 words) [view diff] exact match in snippet view article find links to article

module of a semisimple Lie algebra, or a Weyl module of a reductive algebraic group of positive characteristic. Jantzen filtrations were introduced by

Quasithin group (493 words) [view diff] exact match in snippet view article find links to article

width is usually the rank (the dimension of a maximal torus of the algebraic group). The quasithin groups were classified in a 1221-page paper by Michael

Standard monomial theory (982 words) [view diff] exact match in snippet view article find links to article

over a generalized flag variety or Schubert variety of a reductive algebraic group by giving an explicit basis of elements called standard monomials.

Albert algebra (744 words) [view diff] exact match in snippet view article find links to article

whose automorphism group has identity component the simply-connected algebraic group of type E6. The space of cohomological invariants of Albert algebras

Luna's slice theorem (101 words) [view diff] exact match in snippet view article find links to article

Luna (1973), describes the local behavior of an action of a reductive algebraic group on an affine variety. It is an analogue in algebraic geometry of the

Enriques surface (1,050 words) [view diff] exact match in snippet view article find links to article

(1976). These two extra families are related to the two non-discrete algebraic group schemes of order 2 in characteristic 2. The plurigenera Pn are 1 if

Local trace formula (76 words) [view diff] exact match in snippet view article find links to article

representation of G(F) on the discrete part of L2(G(F)), for G a reductive algebraic group over a local field F. Arthur, James (1991), "A local trace formula"

Converse theorem (513 words) [view diff] exact match in snippet view article find links to article

More generally a converse theorem states that a representation of an algebraic group over the adeles is automorphic whenever the L-functions of various

Symmetric variety (77 words) [view diff] exact match in snippet view article find links to article

space in differential geometry, given by a quotient G/H of a reductive algebraic group G by the subgroup H fixed by some involution of G. Wonderful compactification

Eva Bayer-Fluckiger (310 words) [view diff] exact match in snippet view article find links to article

II regarding the Galois cohomology of a simply-connected semisimple algebraic group when such a group is of classical type. Bayer-Fluckiger was born in

Good filtration (263 words) [view diff] exact match in snippet view article find links to article

good filtration is a filtration of a representation of a reductive algebraic group G such that the subquotients are isomorphic to the spaces of sections

Spherical variety (435 words) [view diff] exact match in snippet view article find links to article

In algebraic geometry, given a reductive algebraic group G and a Borel subgroup B, a spherical variety is a G-variety with an open dense B-orbit. It is

Jacquet–Langlands correspondence (347 words) [view diff] exact match in snippet view article find links to article

the local or global field F. Suppose that G is an inner twist of the algebraic group GL2, in other words the multiplicative group of a quaternion algebra

Arthur–Selberg trace formula (2,147 words) [view diff] exact match in snippet view article find links to article

of L2(G(F)\G(A)) in terms of geometric data, where G is a reductive algebraic group defined over a global field F and A is the ring of adeles of F. There

Steinberg representation (895 words) [view diff] exact match in snippet view article find links to article

denoted by St, is a particular linear representation of a reductive algebraic group over a finite field or local field, or a group with a BN-pair. It is

Equivariant algebraic K-theory (748 words) [view diff] exact match in snippet view article find links to article

coherent sheaves on an algebraic scheme X with action of a linear algebraic group G, via Quillen's Q-construction; thus, by definition, KiG(X)=πi(B+CohG⁡(X))

Mirabolic group (342 words) [view diff] exact match in snippet view article find links to article

word "mirabolic" is a portmanteau of "miraculous parabolic". As an algebraic group, a mirabolic subgroup is the semidirect product of a vector space with

Equivariant sheaf (1,438 words) [view diff] exact match in snippet view article find links to article

the action of G on X to the sheaf F. Moreover, when G is a connected algebraic group, F an invertible sheaf and X is reduced, the cocycle condition is automatic:

Kleiman's theorem (620 words) [view diff] exact match in snippet view article find links to article

factors in the intersection. Precisely, it states: given a connected algebraic group G acting transitively on an algebraic variety X over an algebraically

Representation on coordinate rings (642 words) [view diff] exact match in snippet view article find links to article

closed field k of characteristic zero with the action of a reductive algebraic group G. G then acts on the coordinate ring k[X]{\displaystyle k[X]} of X

Chevalley–Shephard–Todd theorem (858 words) [view diff] exact match in snippet view article find links to article

when a reductive algebraic group acting on a vector space has a polynomial ring of invariants. In the case when the algebraic group is simple all cases

Brauner space (791 words) [view diff] exact match in snippet view article find links to article

space. In the special case when M=G{\displaystyle M=G} is an affine algebraic group, P⋆(G){\displaystyle {\mathcal {P}}^{\star }(G)} becomes an example

Doris Schattschneider (1,210 words) [view diff] case mismatch in snippet view article find links to article

and Ichirô Satake with the thesis, Restricted Roots of a Semi-simple Algebraic Group. She taught at Northwestern University for a year and at the University

Birational invariant (200 words) [view diff] exact match in snippet view article find links to article

it. Reichstein, Z.; Youssin, B. (2002), "A birational invariant for algebraic group actions", Pacific Journal of Mathematics, 204 (1): 223–246, arXiv:math/0007181

Semi-simplicity (1,867 words) [view diff] exact match in snippet view article find links to article

is a direct sum of simple Lie algebras. A semisimple algebraic group is a linear algebraic group whose radical of the identity component is trivial. Semisimple

1 (3,552 words) [view diff] exact match in snippet view article find links to article

Benford's law. 1 is the only known Tamagawa number for a simply connected algebraic group over a number field.[failed verification][page needed] The generating

Hecke algebra of a locally compact group (405 words) [view diff] exact match in snippet view article find links to article

(1965) considered the case when G is a group of points of a reductive algebraic group over a non-archimedean local field F, such as Qp, and K is what is

Longest element of a Coxeter group (374 words) [view diff] exact match in snippet view article find links to article

roots. The open cell Bw0B in the Bruhat decomposition of a semisimple algebraic group G is dense in Zariski topology; topologically, it is the top dimensional

Quasi-split group (153 words) [view diff] exact match in snippet view article find links to article

Linear algebraic group

Torsor (algebraic geometry) (2,535 words) [view diff] exact match in snippet view article

k{\displaystyle k}, G{\displaystyle G} a semisimple, split and simply connected algebraic group (then a group scheme) and P{\displaystyle P} a G{\displaystyle G}-torsor

Quillen–Suslin theorem (645 words) [view diff] exact match in snippet view article find links to article

trivial, this is not true for G-bundles where G is a general reductive algebraic group. "On ignore s'il existe des A-modules projectifs de type fini qui ne

Admissible representation (546 words) [view diff] exact match in snippet view article find links to article

a locally compact totally disconnected group (such as a reductive algebraic group over a nonarchimedean local field or over the finite adeles of a global

Chow group of a stack (1,381 words) [view diff] exact match in snippet view article find links to article

some quasi-projective variety Y with a linearized action of a linear algebraic group G, then the Chow group of X is defined as the G-equivariant Chow group

Jacquet module (369 words) [view diff] exact match in snippet view article find links to article

to classify admissible irreducible representations of a reductive algebraic group G over a local field, and N is the unipotent radical of a parabolic

Fano variety (1,240 words) [view diff] exact match in snippet view article find links to article

variety in characteristic zero that is homogeneous under a linear algebraic group is Fano. The existence of some ample line bundle on X is equivalent

Superstrong (49 words) [view diff] exact match in snippet view article find links to article

to: Superstrong cardinal in set theory Superstrong approximation in algebraic group theory This disambiguation page lists mathematics articles associated

Integer factorization (2,987 words) [view diff] no match in snippet view article find links to article

common flavors to identify group cycles: one by Floyd and one by Brent. Algebraic-group factorization algorithms, among which are Pollard's p − 1 algorithm

Satake isomorphism (861 words) [view diff] exact match in snippet view article find links to article

Classical Satake isomorphism. Let G {\displaystyle G} be a semisimple algebraic group, K {\displaystyle K} be a non-Archimedean local field and O {\displaystyle

Integer factorization (2,987 words) [view diff] no match in snippet view article find links to article

common flavors to identify group cycles: one by Floyd and one by Brent. Algebraic-group factorization algorithms, among which are Pollard's p − 1 algorithm

Slice theorem (differential geometry) (255 words) [view diff] exact match in snippet view article

this metric. Luna's slice theorem, an analogous result for reductive algebraic group actions on algebraic varieties Audin 2004, Theorem I.2.1 On a proof

E. H. Moore Research Article Prize (256 words) [view diff] exact match in snippet view article find links to article

(2008) 2013 Michael J. Larsen and Richard Pink for "Finite subgroups of algebraic group," J. Amer. Math. Soc. (2011) 2016 Caucher Birkar, Paolo Cascini, Christopher

K-theory (4,326 words) [view diff] exact match in snippet view article find links to article

on an algebraic scheme X {\displaystyle X} with action of a linear algebraic group G {\displaystyle G} , via Quillen's Q-construction; thus, by definition

Selberg trace formula (1,605 words) [view diff] exact match in snippet view article find links to article

because this makes the corresponding discrete subgroup Γ into an algebraic group over a field which is technically easier to work with. The case of

Indefinite orthogonal group (1,610 words) [view diff] exact match in snippet view article find links to article

In terms of being a group of Lie type – i.e., construction of an algebraic group from a Lie algebra – split orthogonal groups are Chevalley groups,

Peter Montgomery (mathematician) (620 words) [view diff] no match in snippet view article

factorization, which include a method for speeding up the second stage of algebraic-group factorization algorithms using FFT techniques for fast polynomial evaluation

Parabolic subgroup (55 words) [view diff] exact match in snippet view article find links to article

refer to: a parabolic subgroup of a reflection group a subgroup of an algebraic group that contains a Borel subgroup This disambiguation page lists articles

Nielsen transformation (1,921 words) [view diff] exact match in snippet view article find links to article

Set of mathematical functions concerning algebraic group isomorphism

Algebraic stack (3,504 words) [view diff] exact match in snippet view article find links to article

stacks for algebraic groups are algebraic stacks. In fact, for an algebraic group space G{\displaystyle G} over a scheme S{\displaystyle S} which is

Iwahori–Hecke algebra (2,025 words) [view diff] exact match in snippet view article find links to article

(1965) considered the case when G is a group of points of a reductive algebraic group over a non-archimedean local field K, such as Qp, and K is what is

Stack (mathematics) (5,008 words) [view diff] exact match in snippet view article

[{\text{Spec}}(A)/G]} where G{\displaystyle G} is a linearly reductive algebraic group. This was recently proved to be the case: given a quasi-separated algebraic

Dynkin diagram (5,608 words) [view diff] exact match in snippet view article find links to article

automorphisms need not arise as automorphisms of the corresponding algebraic group, but rather on the level of points valued in a finite field. Diagram

Glossary of symplectic geometry (553 words) [view diff] exact match in snippet view article find links to article

resolution symplectic action A Lie group action (or an action of an algebraic group) that preserves the symplectic form that is present. symplectic reduction

Lie's theorem (2,555 words) [view diff] exact match in snippet view article find links to article

Lie–Kolchin theorem, which is about a (connected) solvable linear algebraic group. Serre 2001, Theorem 3 Humphreys 1972, Ch. II, § 4.1., Corollary A

Homotopy groups of spheres (7,881 words) [view diff] exact match in snippet view article find links to article

map S1↦x are called null homotopic. The classes become an abstract algebraic group with the introduction of addition, defined via an "equator pinch".

Freudenthal magic square (2,837 words) [view diff] exact match in snippet view article find links to article

buildings, which allows one to construct a geometry with any given algebraic group as symmetries, but this requires starting with the Lie groups and constructing

Edwards curve (3,137 words) [view diff] exact match in snippet view article find links to article

equivalent to an elliptic curve in Montgomery form, and thus admits an algebraic group law once one chooses a point to serve as a neutral element. If K is

Nonabelian Hodge correspondence (4,859 words) [view diff] exact match in snippet view article find links to article

principal G{\displaystyle G}-Higgs bundle for a complex reductive algebraic group G{\displaystyle G}, a version of Higgs bundles in the category of principal

Glossary of algebraic topology (7,302 words) [view diff] exact match in snippet view article find links to article

base. character variety The character variety of a group π and an algebraic group G (e.g., a reductive complex Lie group) is the geometric invariant

K-stability (8,027 words) [view diff] exact match in snippet view article find links to article

X⊂CPN{\displaystyle X\subset \mathbb {CP} ^{N}} under the action of a reductive algebraic group G⊂GL⁡(N+1,C){\displaystyle G\subset \operatorname {GL} (N+1,\mathbb

Mutation (Jordan algebra) (15,411 words) [view diff] exact match in snippet view article

complexification of a compact Lie group without center, so a semisimple algebraic group. The identity component H of the compact group acts transitively on

Principalization (algebra) (8,395 words) [view diff] no match in snippet view article

fields with class groups of 2{\displaystyle 2}-rank three. Both, the algebraic, group theoretic access to the principalization problem by Hilbert-Artin-Furtwängler