Double extension of quadratic lie superalgebras

Abstract

In this paper we study Lie superalgebras g with a non-degenerate super-symmetric, consistentg-invariant bilinear form B. Such a (g,B) is called quadratic Lie superalgebra. Our first result generalizes the notion of double extension to quadratic Lie superalgebras. This notion was introduced by Medina and Revoy [8] to study quadratic Lie algebras. In the second theorem, we give a sufficient condition for a quadratic Lie superalgebra to be a double extension. Any nonsimple quadratic Lie superalgebra such that dim is a double extension; also we give an inductive classification of this class of quadratic Lie superalgebras.