Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras
| Autor: | Guo, Hongyan, Li, Haisheng, Tan, Shaobin, Wang, Qing |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we study a family of infinite-dimensional Lie algebras $\widehat{X}_{S}$, 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 $\widehat{X}_{S}$ with what are called the covariant algebras of the affine Lie algebra $\widehat{\mathcal{L}_{S}}$ with respect to some automorphism groups, where $\mathcal{L}_{S}$ is an explicitly defined associative algebra viewed as a Lie algebra. We then show that restricted $\widehat{X}_{S}$-modules of level $\ell$ naturally correspond to equivariant quasi modules for affine vertex algebras related to $\mathcal{L}_{S}$. 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. Comment: 30 pages |
| Databáze: | arXiv |
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