affine algebraic group

An affine algebraic group over a field k is quasi-affine variety G (a locally closed subset of affine space) over k, which is a equipped with a group such that the multiplication map m:G×GG and inverse map i:GG are algebraicMathworldPlanetmath.

For example, k is an affine algebraic group over itself with the group law being addition, and as is k*=k-{0} with the group law multiplication. Other common examples of affine algebraic groups are GLnk, the general linear groupMathworldPlanetmath over k (identifying matrices with affine space) and any algebraic torus over k.

Title affine algebraic group
Canonical name AffineAlgebraicGroup
Date of creation 2013-03-22 13:53:33
Last modified on 2013-03-22 13:53:33
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 7
Author bwebste (988)
Entry type Definition
Classification msc 14L17
Related topic GroupVariety