On the Cohomology of Modular Lie Algebras

摘要

This paper is mainly a survey on the cohomology of modular Lie algebras but there are also several new results. It is intended to be sufficiently self-contained to serve as a first introduction to this topic which plays an important role in modular representation theory. Another goal is to advertise the use of p-envelopes and truncated (co)induced modules in the representation theory of Lie algebras over fields of prime characteristic p. As a main example throughout the paper we consider a series of rank one Lie algebras of Cartan type, the Zassenhaus algebras (which are simple in characteristic p > 2). In the following we will describe the contents of the paper in more detail.