Inductive Description of Quadratic Lie and Pseudo-Euclidean Jordan Triple Systems

Abstract

This chapter is the first investigation of the notion of double extension to triple systems. We appropriate this notion of double extension to quadratic Lie triple systems so that we give an inductive description of all quadratic Lie triple systems. Moreover, we prove that any Jordan triple system is either a \(T^*\)-extension of a Jordan triple system or an ideal of codimension one of a \(T^*\)-extension. Many other results about Lie and Jordan triple systems are offered.