Vertex algebras and extended affine Lie algebras coordinated by rational quantum tori
Vertex algebras and extended affine Lie algebras coordinated by rational quantum tori
复制标题
DOI：
10.1016/j.jalgebra.2020.11.010
复制
发表时间：
2021-03
影响因子：
0.9
通讯作者：
Fulin Chen;X. Liao;Shaobin Tan;Qing Wang
中科院分区：
文献类型：
--
作者：
Fulin Chen;X. Liao;Shaobin Tan;Qing Wang
设sl Nˆ(C Q)是由有理量子2-环面Cq协调的AN−1型扩展仿射李代数的核心.本文首先证明了对任意复数ℓ，限制sl Nˆ(C Q)-模范则同构于由共形李代数Cg产生的顶点代数V C gℓ，0)的扭模范畴，其中C gˆ(ℓ同构于环状李代数.证明了对于任意非负整数ℓ，水平ˆ的可积限制sl Nℓ(C Q)-模正是V C gˆ(ℓ，0)的商顶点代数的扭模.最后，我们对不可约分次扭L C gˆ(ℓ，0)-模进行了分类。
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.