$(G,χ_ϕ)$-equivariant $ϕ$-coordinated quasi modules for nonlocal vertex algebras

$(G,χ_ϕ)$-equivariant $ϕ$-coordinated modules for vertex algebras

To give a unified treatment on the association of Lie algebras and vertex algebras, we study $(G,χ_ϕ)$-equivariant $ϕ$-coordinated quasi modules for vertex algebras, where $G$ is a group with $χ_ϕ$ a linear character of $G$ and $ϕ$ is an associate of the one-dimensional additive formal group. The theory of $(G,χ_ϕ)$-equivariant $ϕ$-coordinated quasi modules for nonlocal vertex algebra is established in \cite{JKLT}. In this paper, we concentrate on the context of vertex algebras. We establish several conceptual results, including a generalized commutator formula and a general construction of ve…

Extended affine Lie algebras, vertex algebras and equivariant $ϕ$-coordinated quasi modules

For any nullity $2$ extended affine Lie algebra $\mathcal{E}$ of maximal type and $\ell\in\mathbb{C}$, we prove that there exist a vertex algebra $V_{\mathcal{E}}(\ell)$ and an automorphism group $G$ of $V_{\mathcal{E}}(\ell)$ equipped with a linear character $χ$, such that the category of restricted $\mathcal{E}$-modules of level $\ell$ is canonically isomorphic to the category of $(G,χ)$-equivariant $ϕ$-coordinated quasi $V_{\mathcal{E}}(\ell)$-modules. Moreover, when $\ell$ is a nonnegative integer, there is a quotient vertex algebra $L_{\mathcal{E}}(\ell)$ of $V_{\mathcal{E}}(\ell)$ modulo…

扭曲的量子 affine 代数与量子顶点代数的 equivariant ϕ-协调模

Twisted quantum affine algebras and equivariant $ϕ$-coordinated modules for quantum vertex algebras

本文研究量子 affine 代数与量子顶点代数的自然联系，提出 ϕ-协调准模的 ϳ-adic 构造，并构建了 ϳ-adic 量子顶点代数 V_L[[ℏ]]^η 及其与扭曲量子 affine 代数的关联。

量子顶点代数及其Φ-协调拟模

Quantum vertex algebras and their phi-coordinated quasi modules

我们发展了一个非局部顶点代数的$ϕ$ -协调（拟）模理论，并建立了非局部顶点代数及其$ϕ$ -协调（拟）模的概念结构，其中$ϕ$是我们称之为一维加性形式群的一个伴随.通过将$ϕ$特殊化到一个特定的结合体上，我们得到了一个新的弱量子顶点代数的构造，它是\cite{li-qva1}意义下的。作为应用，我们将弱量子顶点代数与量子仿射代数联系起来，并将量子顶点代数和$ϕ$ -协调模与某个量子$βγ$ -系统联系起来。

通过顶点双代数形变顶点代数

Deforming vertex algebras by vertex bialgebras

本文研究右 H-余模非局部顶点代数，构造兼具相容 H-模结构的顶点代数形变及碎积代数的 ϕ-协调拟模，并由非退化偶格得到量子顶点代数族。

与量子环面$\boldsymbol{\frak{gl}}_N$相关的量子顶点代数

Quantum vertex algebra associated to quantum toroidal $\mathfrak{gl}_N$

本研究通过等变φ-坐标拟模，形变泛仿射顶点代数构造出ℏ-进量子Z-顶点代数，证明水平为ℓ的限制gl_N型量子环面代数模的范畴与该量子顶点代数的等变拟模范畴典范同构，建立了二者的关联。