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Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori
- Source :
- Canadian Journal of Mathematics. 58:225-248
- Publication Year :
- 2006
- Publisher :
- Canadian Mathematical Society, 2006.
-
Abstract
- 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 themin 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.
- Subjects :
- Pure mathematics
Computer Science::Information Retrieval
General Mathematics
Simple Lie group
010102 general mathematics
Killing form
01 natural sciences
Affine Lie algebra
Lie conformal algebra
Reductive Lie algebra
Algebra
Adjoint representation of a Lie algebra
Representation of a Lie group
0103 physical sciences
010307 mathematical physics
0101 mathematics
Generalized Kac–Moody algebra
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........41e6c4d76115db9de2ddd738df616259