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×G→G and inverse map i:G→G are algebraic.
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 group over k (identifying matrices with affine space) and any algebraic torus over k.
Title | affine algebraic group |
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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 |