Quadratic Lie superalgebras with reductive even part

Abstract

The aim of this paper is to exibit some non trivial examples of quadratic Lie superalgebras such that the even part is a reductive Lie algebra and the action of the even part on the odd part is not completely reducible and to give an inductive classi cation of this class of quadratic Lie superalgebras. The notion of generalized double extension of quadratic Lie superalgebras proposed by I. Bajo, S. Benayadi and M. Bordemann [1] has a crucial importance in this work. In particular we will improve some results of [4], in the sense that we will not demand that the action of the even part on the odd part is completely reducible, which naturally makes the proofs of our results more diffcult.