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Vertex algebras and extended affine Lie algebras coordinated by rational quantum tori.
- Source :
-
Journal of Algebra . Mar2021, Vol. 569, p111-142. 32p. - Publication Year :
- 2021
-
Abstract
- Let sl N ˆ (C q) be the core of extended affine Lie algebra of type A N − 1 coordinated by the rational quantum 2-torus C q. In this paper, we first prove that for any complex number ℓ , the category of restricted sl N ˆ (C q) -modules of level ℓ is canonically isomorphic to the category of twisted modules for the vertex algebra V C g ˆ (ℓ , 0) arising from a conformal Lie algebra C g , where C g ˆ is isomorphic to a toroidal Lie algebra. Then we prove that for any nonnegative integer ℓ , the integrable restricted sl N ˆ (C q) -modules of level ℓ are exactly the twisted modules for the quotient vertex algebra L C g ˆ (ℓ , 0) of V C g ˆ (ℓ , 0). Finally, we classify irreducible graded twisted L C g ˆ (ℓ , 0) -modules. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 569
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 147604871
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2020.11.010