ABSTRACT
This chapter discusses the structure of a general algebraic Lie algebra. Lie correspondence works very well in characteristic 0, but is notably less powerful in positive characteristic. The chapter presents a number of results on the Lie correspondence, as well as on algebraic Lie algebras. One of the cornerstones of this theory is the unique smallest algebraic group whose Lie algebra contains a given element. The chapter deals with algorithmic problems. It shows some of the main results that make the Lie correspondence so effective in characteristic 0. The Lie correspondence makes it possible to obtain the corresponding information for an algebraic group. The chapter describes an algorithm for finding a generating set and applies it to find algorithms for computing the centralizer and normalizer of an algebraic subgroup of an algebraic group. Recall that algebraic groups are closed under the multiplicative Jordan decomposition.
