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Structure and representation for a class of infinite-dimensional Lie algebras
- Source :
-
Journal of Algebra . Jan2007, Vol. 307 Issue 2, p804-828. 25p. - Publication Year :
- 2007
-
Abstract
- Abstract: Let be a commutative associative algebra over the complex field C, and be the complexification of the real Lie algebra . For any fixed elements , we define a Lie algebra with Lie bracket given by (1.2). When the associative algebra is the Laurent polynomial algebra , we determine its derivation Lie algebra , and universal central extension . We also give a vertex operator representation for the Lie algebra . This new class of Lie algebras includes the affine Lie algebra and the toroidal Lie algebras of type . We note that in general this kind of Lie algebras is not -graded. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICAL analysis
*LINEAR algebra
*MATHEMATICS
*CALCULUS of operations
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 307
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 23277770
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2006.05.013