Lie Algebras and Algebraic Subgroups

Abstract

This chapter establishes the Lie algebra technique for the structure and representation theory of algebraic groups. Section 1 contains only special field-theoretical preparations. Section 2 develops the connections between the algebraic subgroups of an algebraic group G and the sub Lie algebras of L(G) fully, under the assumption that the base field be of characteristic 0. This assumption is retained in Section 3, which is devoted to reducing, as far as is possible in general, the representation theory of an algebraic group to that of its Lie algebra.