A Generalization of Tits' Construction of Lie Algebras by Jordan Algebras to Jordan Triple Systems

Abstract

We describe a generalization of Tits' construction of Lie algebras by Jordan algebras ([4]) to a construction of Lie Algebras by Jordan triple systems. This generalization comprises Meyberg's construction of Lie algebras by Jordan triple systems ([3]) in the same way as Tits' construction comprises Kantor's ([1]) and Koecher's ([2]), and it has as Tits' construction the advantage that it allows to obtain different forms of a Lie algebra starting with the same Jordan triple system.