Solvable Pseudo-Euclidean Jordan Superalgebras

Abstract

Jordan superalgebras which are endowed with an even nondegenerate supersymmetric associative bilinear form are called pseudo-Euclidean Jordan superalgebras. In this work, we introduce the notion of T*-extension of Jordan superalgebras to give some examples of such superalgebras. The main result of this article is to give an inductive description of solvable pseudo-Euclidean Jordan superalgebras. We obtain this description by introducing the notions of double extension and generalized double extension of Jordan superalgebras.