Atlas: Functional Analysis in Lie Theory by Antonio-Jesus Calderon-Martin

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Functional Analysis Valencia 2000
July 3-7, 2000
Technical University of Valencia (UPV) and University of Valencia (UV)
Valencia, Spain

Organizers
R.M. Aron (Kent State U., USA), K.D. Bierstedt (U. Paderborn, Germany), J. Bonet (UPV), J. Cerdà (U. Barcelona, Spain), H. Jarchow (U. Zürich, Switzerland), M. Maestre (UV), J. Schmets (U. Liège, Belgium)

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Functional Analysis in Lie Theory
by
Antonio-Jesús Calderón-Martín
Universidad de Cádiz
Coauthors: Cándido Martín González (Universidad de Málaga)

In [1], Lister introduces the concept of Lie triple system. He classified the finite-dimensional simple Lie triple systems over an algebraically closed field of characteristic zero. Neher also studies Lie triple systems and their relations with Jordan triple systems in [2]. 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 prove, using Jordan H^*-pairs techniques, that every infinite-dimensional topologically simple L^*-triple, verifying an additional property, has a two-graded L^*-algebra envelope 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.

2. E. Neher, On the classification of Lie and Jordan triple systems, Comm. in Algebra. Vol. no. 13 (12), 2615-2667.

MSC: 46K70, 46L70

(T)

Date received: April 13, 2000