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q-Virasoro algebra and affine Kac-Moody Lie algebras.
- Source :
-
Journal of Algebra . Sep2019, Vol. 534, p168-189. 22p. - Publication Year :
- 2019
-
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 g S ˆ (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 2 l + 1 , D S is isomorphic to the affine Kac-Moody algebra of type B l (1). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 534
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 137475748
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2019.06.009