The object of this section is to attach to an algebraic group a Lie algebra (in a suitably functorial way). For our purpose, a Lie algebra over K is a subspace of an associative K-algebra which is closed under the bracket operation [x, y] = xy − yx. An important example is the general linear algebra gl(n, K), which is the associative algebra M(n, K) viewed as Lie algebra. (This will turn out to be essentially the Lie algebra of GL(n, K).)
KeywordsTangent Space Tangent Vector Algebraic Group Closed Subgroup Affine Space
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