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On involutive Lie algebras having a Cartan decomposition

Published online by Cambridge University Press:  17 April 2009

A. J. Calderón Martín
A. J. Calderón Martín
Affiliation:
Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Cádiz e-mail: [email protected]
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We introduce the concept of Cartan decomposition relative to a Cartan subalgebra H in the sense of Y. Billig and A. Pianzola for involutive complex Lie algebras L of arbitrary dimension. If L has such a decomposition and is infinite dimensional and simple, we show it is *-isomorphic to a direct limit of classical finite dimensional simple involutive Lie algebras of the same type A, B, C, or D.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 191 - 202
Copyright
Copyright © Australian Mathematical Society 2004

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