Generalized Reduced Enveloping Algebras for Restricted Lie Algebras

We observe that any finite-dimensional indecomposable module for a restricted Lie algebra over an algebraically closed field is a module for a finite-dimensional quotient of the universal enveloping algebra. These algebras form a two-parameter family which generalizes the notion of a reduced enveloping algebra. We identify each such algebra as a reduced enveloping algebra for an associated Lie algebra and use this to compute support varieties and obtain some representation-theoretic consequences.