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Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori

Published online by Cambridge University Press:  20 November 2018

Saeid Azam
Saeid Azam*
Affiliation:
Department of Mathematics, University of Isfahan, P.O. Box 81745, Isfahan, Iran e-mail: saiedazam@yahoo.comazam@sci.ui.ac.ir Institute for Theoretical Physics and Mathematics (IPM)
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Abstract

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We investigate a class of Lie algebras which we call generalized reductive Lie algebras. These are generalizations of semi-simple, reductive, and affine Kac–Moody Lie algebras. A generalized reductive Lie algebra which has an irreducible root system is said to be irreducible and we note that this class of algebras has been under intensive investigation in recent years. They have also been called extended affine Lie algebras. The larger class of generalized reductive Lie algebras has not been so intensively investigated. We study them in this paper and note that one way they arise is as fixed point subalgebras of finite order automorphisms. We show that the core modulo the center of a generalized reductive Lie algebra is a direct sum of centerless Lie tori. Therefore one can use the results known about the classification of centerless Lie tori to classify the cores modulo centers of generalized reductive Lie algebras.

Keywords

17B6517B6717B40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 2 , 01 April 2006 , pp. 225 - 248
Copyright
Copyright © Canadian Mathematical Society 2006

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