On generalized reduced representations of restricted Lie superalgebras in prime characteristic

Document Type : Research Paper


1 Department of Mathematics‎, ‎Shanghai Maritime University‎, ‎Shanghai 201306‎, ‎China

2 School of Fundamental Studies‎, ‎Shanghai University of Engineering Science‎, ‎Shanghai 201620‎, ‎China


Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed 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.


Main Subjects