Back to Search
Start Over
Trigonometric Lie algebras, affine Lie algebras, and vertex algebras.
- Source :
-
Advances in Mathematics . Mar2020, Vol. 363, pN.PAG-N.PAG. 1p. - Publication Year :
- 2020
-
Abstract
- In this paper, we explore natural connections among trigonometric Lie algebras, (general) affine Lie algebras, and vertex algebras. Among the main results, we obtain a realization of trigonometric Lie algebras as what were called the covariant algebras of the affine Lie algebra A ˆ of Lie algebra A = gl ∞ ⊕ gl ∞ with respect to certain automorphism groups. We then prove that restricted modules of level ℓ for trigonometric Lie algebras naturally correspond to equivariant quasi modules for the affine vertex algebras V A ˆ (ℓ , 0) (or V A ˆ (2 ℓ , 0)). Furthermore, we determine irreducible modules and equivariant quasi modules for the simple vertex algebra L A ˆ (ℓ , 0) with ℓ a positive integer. In particular, we prove that every quasi-finite unitary highest weight (irreducible) module of level ℓ for type A trigonometric Lie algebra gives rise to an irreducible equivariant quasi L A ˆ (ℓ , 0) -module. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LIE algebras
*ALGEBRA
*AUTOMORPHISM groups
Subjects
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 363
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 141636569
- Full Text :
- https://doi.org/10.1016/j.aim.2020.106985