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Algebraic group

In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory.

Definitions, Affine algebraic groups & Overview

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Overview

Definitions

Affine algebraic groups

Abelian varieties

Structure theorem for general algebraic groups

Connectedness

Algebraic groups over local fields and Lie groups

Coxeter groups and algebraic groups

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Map overview Semantic statistics

Algebraic group

Nodes80
Edges79
Triples100
Avg. degree1.98
Density0.025
Components1

How this topic connects Entity context

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Algebraic group

Top relations

related to References · 48
Algebraic group → Abelian, Affine Group Schemes, Algebraic Groups, André, Arithmetic SubgroupsMumford, Armand, Berlin, Birkhäuser Boston, Boston, Cambridge University Press, Chevalley, Chevalley's, Classification, Claude, Courbes, David, Field, Finite Type, Graduate Texts, Group Schemes
related to Algebraic groups over local fields and Lie groups · 8
Algebraic group → An, Heisenberg, If, Lie, Not, SL2, Such, This
related to Affine algebraic groups · 5
Algebraic group → Among, An, For, GL, Using
related to Connectedness · 5
Algebraic group → An, As, For, It, Zariski
related to Examples · 5
Algebraic group → GL, It, Let, SL, The
related to Lie algebra of an algebraic group · 5
Algebraic group → As, In, Lie, Similarly, The Lie
related to Structure theorem for general algebraic groups · 4
Algebraic group → Chevalley's, G/H, More, Not
is a · 3
Algebraic group → algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety, extension of an abelian variety by a linear algebraic group, linear
related to Abelian varieties · 3
Algebraic group → Abelian, Jacobian, They
related to Coxeter groups and algebraic groups · 3
Algebraic group → Coxeter, There, This

Important terminology Word statistics

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Important terminology

algebraic group groups displaystyle mathrm linear variety affine general field lie varieties subgroup abelian mathbb projective structure also connected every

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Algebraic groupis aalgebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety0.90text
Algebraic groupis alinear0.90text
Algebraic groupis aextension of an abelian variety by a linear algebraic group0.90text
that of invertible triangular matrices.Linear algebraic groups can be classified to a certain extentinstance ofor some solvable groups0.80text
Algebraic grouprelated to Abelian varietiesAbelian0.60section
Algebraic grouprelated to Abelian varietiesThey0.60section
Algebraic grouprelated to Abelian varietiesJacobian0.60section
Algebraic grouprelated to Affine algebraic groupsAn0.60section
Algebraic grouprelated to Affine algebraic groupsAmong0.60section
Algebraic grouprelated to Affine algebraic groupsUsing0.60section
Algebraic grouprelated to Affine algebraic groupsFor0.60section
Algebraic grouprelated to Affine algebraic groupsGL0.60section

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