论文标题
在任意字段上，顶点操作员代数的内态特性
Endomorphism property of vertex operator algebras over arbitrary fields
论文作者
论文摘要
在本文中，我们在任意字段$ \ mathbb {f} $上研究了顶点操作员代数的内态属性，并使用$ \ text {char}（\ mathbb {f}）\ neq 2 $。让$ v $是超过$ \ mathbb {f} $的有限生成的顶点操作员代数，而$ m $是一种不可减至的可允许$ v $ -module。我们证明，$ \ text {end} _v（m）$中的每个元素都是$ \ mathbb {f} $的代数，而$ \ text {end} _v（m）$也是有限的。作为一个应用程序，我们证明了Schur在任意代数封闭的字段上有限有限生成的顶点操作员代数的引理，并且我们对$ V $ - 模块的绝对不可约性进行了测试。
In this paper, we study the endomorphism properties of vertex operator algebras over an arbitrary field $\mathbb{F}$, with $\text{Char}(\mathbb{F}) \neq 2$. Let $V$ be a strongly finitely generated vertex operator algebra over $\mathbb{F}$, and $M$ be an irreducible admissible $V$-module. We prove that every element in $\text{End}_V(M)$ is algebraic over $\mathbb{F}$ and that $\text{End}_V(M)$ is also finite-dimensional. As an application, we prove Schur's lemma for strongly finitely generated vertex operator algebras over arbitrary algebraically closed fields, and we give a test for absolute irreducibility of $V$-modules.
