扭Zhu代数与双模的Noetherian性

扭状正则表示与顶点算子代数理论中的双模

Twisted regular representations and bimodules in vertex operator algebra theory

本文利用顶点算子代数的扭状正则表示理论，构建扭状Zhu代数上的双模，扩展了Li在非扭情况下的工作，并证实了Dong和Jiang关于双模理论的猜想。

关于扭曲Zhu代数的双模与顶点算子代数的扭曲融合规则定理

Bimodules over twisted Zhu algebras and twisted fusion rules theorem for vertex operator algebras

本文研究了扭曲Zhu代数上的双模构造，并基于此推导出顶点算子代数的扭曲融合规则定理，通过构造特定模并证明其子模的universal性质。

A proof of the fusion rules theorem

We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the same data. This provides a new proof and alternative version of Frenkel and Zhu's fusion rules theorem in terms of the dimension of certain bimodules over Zhu's algebra, without the assumption of rationality.

手性代数的节点退化 II：局部结构与手性Zhu代数

Nodal degeneration of chiral algebras II: Local structure and chiral Zhu algebras

本文通过几何构造将顶点代数的Zhu代数推广到因子化代数，定义了一个导出结合代数及其手性双模，并证明其零阶同调恢复节点处顶点代数的模式转移代数。

On resolution of highest weight modules over the $\mathcal{N}=2$ superconformal algebra

In this paper we construct Bernstein--Gelfand--Gelfand type resolution of simple highest weight modules over the simple $\mathcal{N}=2$ vertex operator superalgebra of central charge $c_{p,p'}=3\left(1-\frac{2p'}{p}\right)$ by means of the Kazama--Suzuki coset construction. As an application, we compute the twisted Zhu algebras of the simple $\mathcal{N}=2$ vertex operator superalgebra. We also compute the Frenkel--Zhu bimodule structure associated with a certain simple highest weight module of central charge $c_{3,2}=-1$.

顶点代数的扭曲ϕ-协调模与朱对应的定理

Twisted $ϕ$-coordinated modules for vertex algebras and Zhu's correspondence theorem

本文研究了顶点代数中扭曲ϕ-协调模的构造及其与朱对应定理的关系，证明了简单模与不可约模之间的双射关系。