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Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras.
- Source :
-
Journal of Algebra . Dec2023, Vol. 636, p42-74. 33p. - Publication Year :
- 2023
-
Abstract
- In this paper, we study a family of infinite-dimensional Lie algebras X ˆ S , where X stands for the type: A , B , C , D , and S is an abelian group, which generalize the A , B , C , D series of trigonometric Lie algebras. Among the main results, we identify X ˆ S with what are called the covariant algebras of the affine Lie algebra L S ˆ with respect to some automorphism groups, where L S is an explicitly defined associative algebra viewed as a Lie algebra. We then show that restricted X ˆ S -modules of level ℓ naturally correspond to equivariant quasi modules for affine vertex algebras related to L S. Furthermore, for any finite cyclic group S , we completely determine the structures of these four families of Lie algebras, showing that they are essentially affine Kac-Moody Lie algebras of certain types. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 636
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 172778650
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2023.07.041