Computations in Associative and Lie Algebras

Abstract

In this chapter we consider some basic algorithmic problems related to finite dimensional associative algebras. Our starting point is the structure theory of these algebras. This theory gives a description of the main structural ingredients of finite dimensional associative algebras, and specifies the way the algebra is constructed from these building blocks. We describe polynomial time algorithms to find the main components: the Jacobson radical and the simple direct summands of the radical-free part.