Restricted Lie algebras with bounded cohomology and related classes of algebras

Abstract

We determine the structure of restricted Lie algebras with bounded cohomology over arbitrary fields of prime characteristic. As a byproduct a classification of the serial restricted Lie algebras and the restricted Lie algebras of finite representation type is obtained. In addition, we derive complete information on the finite dimensional indecomposable restricted modules of these algebras over algebraically closed fields.