Simple toroidal vertex algebras and their irreducible modules
Simple toroidal vertex algebras and their irreducible modules
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简单环形顶点代数及其不可约模
DOI：
10.1016/j.jalgebra.2015.05.024
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发表时间：
2015
影响因子：
0.9
通讯作者：
Wang Qing
中科院分区：
文献类型：
--
作者：
Kong Fei;Li Haisheng;Tan Shaobin;Wang Qing
In this paper, we continue the study on toroidal vertex algebras initiated in [15], to study concrete toroidal vertex algebras associated to toroidal Lie algebra L r (g ˆ)= g ˆ⊗ L r, where g ˆ is an untwisted affine Lie algebra and L r= C [t 1±1,…, t r±1]. We first construct an (r+ 1)-toroidal vertex algebra V (T, 0) and show that the category of restricted L r (g ˆ)-modules is canonically isomorphic to that of V (T, 0)-modules. Let c denote the standard central element of g ˆ and set S c= U (L r (C c)). We furthermore study a distinguished subalgebra of V (T, 0), denoted by V (S c, 0). We show that (graded) simple quotient toroidal vertex algebras of V (S c, 0) are parametrized by a Z r-graded ring homomorphism ψ: S c→ L r such that Imψ is a Z r-graded simple S c-module. Denote by L (ψ, 0) the simple quotient (r+ 1)-toroidal vertex algebra of V (S c, 0) associated to ψ. We determine for which ψ, L (ψ, 0) is an integrable L r (g ˆ)-module and we then classify irreducible L (ψ, 0)-modules for such a ψ. For our need, we also obtain various general results.
