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 $m:G\\times G\\to G$ and inverse map $i:G\\to G$ 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 $\\mathrm{GL}_{n}k$ , the general linear group over $k$ (identifying matrices with affine space) and any algebraic torus over $k$ .

单词	AffineAlgebraicGroup
释义	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 $m:G\\times G\\to G$ and inverse map $i:G\\to G$ 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 $\\mathrm{GL}_{n}k$ , the general linear group over $k$ (identifying matrices with affine space) and any algebraic torus over $k$ .
随便看	SimpleAlgebraicSystem simple algebraic system SimpleAndSemisimpleLieAlgebras simple and semi-simple Lie algebras SimpleBoundaryPoint simple boundary point SimpleExampleOfComposedConformalMapping simple example of composed conformal mapping SimpleFieldExtension simple field extension SimpleFunction simple function SimpleGroup simple group SimpleGroups Simple Groups SimpleInterest simple interest SimpleModule simple module SimplePath simple path SimplePole simple pole SimplePredictableProcess