An Introduction to Universal Central Extensions of Lie Superalgebras

Abstract

We provide an introduction to the theory of universal central extensions of Lie superalgebras. In particular, we show that a Lie superalgebra has a universal central extension if and only if it is perfect. We also consider the question of lifting automorphisms and derivations to the universal central extension, and describe the universal central extension of a semidirect product.KeywordsLie superalgebrasuniversal central extension