Enveloping algebras of Lie superalgebras

Abstract

We review elementary properties of Lie superalgebras and their representations. These are later used in a discussion of the enveloping algebra U(L) of a Lie superalgebra L from the point of view of non-commutative ring theory. In particular, we show that U(L) has an Artinian ring of quotients, that Harish-Chandra's theorem holds for U(L) and that in several cases gl.dim(/(L)) turns out to be infinite.