Back to Search
Start Over
The Jordan socle and finitary Lie algebras
- Source :
-
Journal of Algebra . Oct2004, Vol. 280 Issue 2, p635-654. 20p. - Publication Year :
- 2004
-
Abstract
- Abstract: In this paper we introduce the notion of Jordan socle for nondegenerate Lie algebras, which extends the definition of socle given in [A. Fernández López et al., 3-Graded Lie algebras with Jordan finiteness conditions, Comm. Algebra, in press] for 3-graded Lie algebras. Any nondegenerate Lie algebra with essential Jordan socle is an essential subdirect product of strongly prime ones having nonzero Jordan socle. These last algebras are described, up to exceptional cases, in terms of simple Lie algebras of finite rank operators and their algebras of derivations. When working with Lie algebras which are infinite dimensional over an algebraically closed field of characteristic 0, the exceptions disappear and the algebras of derivations are computed. [Copyright &y& Elsevier]
- Subjects :
- *LIE algebras
*LINEAR algebra
*MATHEMATICAL analysis
*MATHEMATICS
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 280
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 19238901
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2004.06.013