Enveloping algebras of Lie superalgebras

Erazm Jerzy Behr

Vol. 130 (1987), No. 1, 9–25

DOI: 10.2140/pjm.1987.130.9

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(U(L)) turns out to be infinite.

Mathematical Subject Classification 2000

Primary: 17B99

Secondary: 17A70, 16A08

Milestones

Received: 8 May 1986

Published: 1 November 1987