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arXiv · 2211.16573

Endomorphism property of vertex operator algebras over arbitrary fields

Chao Yang·Jianqi Liu
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Abstract

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.

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Chao Yang, Jianqi Liu. 2022-11-29. Endomorphism property of vertex operator algebras over arbitrary fields. https://arxiv.org/abs/2211.16573

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