On generalized reduced representations of restricted Lie superalgebras in prime characteristic

‎Let $\mathbb{F}$ be an algebraically closed field of prime‎ ‎characteristic $p > 2$ and $(\ggg‎, ‎[p])$ a finite-dimensional‎ ‎restricted Lie superalgebra over $\mathbb{F}$‎. ‎It is shown that any‎ ‎finite-dimensional indecomposable $\ggg$-module is a module for a‎ ‎finite-dimensional quotient of the universal enveloping superalgebra‎ ‎of $\ggg$‎. ‎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.