DIFFERENTIABLY SIMPLE LIE-SUPERALGEBRAS AND REPRESENTATIONS OF SEMISIMPLE LIE-SUPERALGEBRAS

The purpose of this paper is two-fold. First it supplies the proof of Kac's classification theorem of finite dimensional differentiably simple Lie superalgebras of characteristic 0. Next, we use this theorem to obtain a classification of finite dimensional representations of semisimple Lie superalgebras whose simple components are simple Lie superalgebras which have only inner derivations. (C) 1995 Academic Press, Inc.