## Abstract

In this paper, we introduce an infinite-dimensional Lie algebra D_{S} for any abelian group S. If S is the additive group of integers, D_{S} reduces to the q-Virasoro algebra D_{q} introduced by Belov and Chaltikian in the study of lattice conformal theories. Guided by the theory of equivariant quasi modules for vertex algebras, we introduce another Lie algebra g_{S} with S as an automorphism group and we prove that D_{S} is isomorphic to the S-covariant algebra of the affine Lie algebra g_{S}ˆ. We then relate restricted D_{S}-modules of level ℓ∈C to equivariant quasi modules for the vertex algebra V_{gSˆ}(ℓ,0) associated to g_{S}ˆ with level ℓ. Furthermore, we establish an intrinsic connection between the q-Virasoro algebra D_{q} and affine Kac-Moody Lie algebras. More specifically, we show that if S is a finite abelian group of order 2l+1, D_{S} is isomorphic to the affine Kac-Moody algebra of type B_{l} ^{(1)}.

Original language | English (US) |
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Pages (from-to) | 168-189 |

Number of pages | 22 |

Journal | Journal of Algebra |

Volume | 534 |

DOIs | |

State | Published - Sep 15 2019 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

## Keywords

- Affine Kac-Moody Lie algebras
- Vertex algebras
- q-Virasoro algebra