Complete sets of representations of classical Lie superalgebras
A collection of modules over a finite-dimensional complex Lie superalgebra is said to be complete if for every element \(u\neq 0\) in the enveloping algebra there exists a module \(V\) in the collection such that \(u\cdot V\neq 0\). Here it is shown that the finite-dimensional irreducible modules over a finite-dimensional complex Lie superalgebra form a complete set if and only if the even part of the Lie superalgebra is reductive and the universal enveloping algebra is semiprime. For classical Lie superalgebras, these sets are characterized in more detail.
scientific article; zbMATH DE number 606909