On two-graded L*-Algebras and L*-Triple Systems
by
Antonio Jesus Calderón Martín
Universidad de Cádiz
Coauthors: C. Martín González (Universidad de Málaga)

In [1], Lister introduced the concept of Lie triple system and classified the finite-dimensional simple Lie triple systems over an algebraically closed field of characteristic zero. In order to study infinite-dimensional Lie triple systems, we introduce the notion of L*-triple, as a mixture between a Lie triple system and a Hilbert space, and obtain a classification of L*-triples admitting a two-graded L*-algebra envelope. However, the problem on the existence of L*-algebra envelopes is still open. We study several classes of L*-triples that admit two-graded L*-algebra envelopes and then, we classify them.

References:

1. W.G. Lister, A structure theory of Lie triple systems, Trans. Amer. Math. Soc. 72 (1952) 217-242.

Date received: February 23, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cage-07.