Relative Cohomology of Algebraic Linear Groups, II

First non-abelian cohomology of topological groups II

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

Detecting Rational Cohomology of Algebraic Groups

Let G be a connected, semisimple algebraic group defined over an algebraically closed field k of positive characteristic p. Assume that G is defined and split over the prime field k0 = GF (p), and for q = p , let G(q) be the subgroup of GF (g)-rational points. Let V be a rational G-module, and, for a non-negative integer r, let V(r) be the rational G-module obtained by 'twisting' the original G...

Linear Algebraic Groups

Linear Algebraic Groups

Linear Algebraic Groups

We give a summary, without proofs, of basic properties of linear algebraic groups, with particular emphasis on reductive algebraic groups.