Vertex algebras and TKK algebras
Vertex algebras and TKK algebras
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DOI：
10.1016/j.jalgebra.2023.10.027
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发表时间：
2023-07
影响因子：
0.9
通讯作者：
Fulin Chen;Lingen Ding;Qing Wang
中科院分区：
文献类型：
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作者：
Fulin Chen;Lingen Ding;Qing Wang
本文通过扭模将TKK代数G_n（J）与顶点代数联系起来.首先，我们证明了对任意复数<$1，水平<$1的限制G <$（J）-模范畴与σ-扭曲V C g <$（<$，0）-模范畴正则同构，其中V C g <$（<$，0）是由C2型环面李代数产生的顶点代数，σ是V C g <$（<$，0）的同构，0），从而导出了该环面李代数的对合。其次，证明了对任意非负整数<$1，水平<$1的可积限制G <$（J）-模恰为VC g <$（<$，0）的商顶点代数L C g <$（<$，0）的σ-扭模.最后，我们对不可约12 N-分次σ-扭LCg <$（<$，0）-模进行了分类.
In this paper, we associate the TKK algebra G ˆ (J) with vertex algebras through twisted modules. Firstly, we prove that for any complex number ℓ, the category of restricted G ˆ (J)-modules of level ℓ is canonically isomorphic to the category of σ-twisted V C g ˆ (ℓ, 0)-modules, where V C g ˆ (ℓ, 0) is a vertex algebra arising from the toroidal Lie algebra of type C 2 and σ is an isomorphism of V C g ˆ (ℓ, 0) induced from the involution of this toroidal Lie algebra. Secondly, we prove that for any nonnegative integer ℓ, the integrable restricted G ˆ (J)-modules of level ℓ are exactly the σ-twisted modules for the quotient vertex algebra L C g ˆ (ℓ, 0) of V C g ˆ (ℓ, 0). Finally, we classify the irreducible 1 2 N-graded σ-twisted L C g ˆ (ℓ, 0)-modules.