Finite dimensional compact and unitary Lie superalgebras

Abstract

Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is achieved by describing the classification of real finite dimensional compact simple Lie superalgebras, and analyzing, in a rather elementary and direct way, the decomposition of reductive Lie superalgebras (g is a semisimple g0--module) over fields of characteristic zero into ideals. © 2015 Elsevier B.V.