On generalized reduced representations of restricted Lie superalgebras in prime characteristic

Let F be an algebraically closed field of prime characteristic p > 2 and (g, [p]) a finite-dimensional restricted Lie superalgebra over F. It is shown that any finite-dimensional indecomposable g-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of g. These quotient superalgebras are called the generalized reduced enveloping superalgebras, which generalize the notion of reduced enveloping superalgebras. Properties and representations of these generalized reduced enveloping superalgebras are studied. Moreover, each such superalgebra can be identified as a reduced enveloping superalgebra of the associated restricted Lie superalgebra.