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Bibliographic Details
Main Author: Yang, Chao
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.03989
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author Yang, Chao
author_facet Yang, Chao
contents This paper investigates Y(z)-injective vertex superalgebras. We first establish that two fundamental classes of vertex superalgebras -- simple ones and those admitting a PBW basis -- are Y(z)-injective. We then study actions of Hopf algebras on Y(z)-injective vertex superalgebras and prove that every finite-dimensional Hopf algebra acting inner faithfully on such algebras must be a group algebra. As a direct consequence, the study of the structure and representation theory of fixed-point subalgebras under finite-dimensional Hopf algebra actions reduces to that under group actions.
format Preprint
id arxiv_https___arxiv_org_abs_2509_03989
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Y(z)-injective vertex superalgebras and Hopf actions
Yang, Chao
Quantum Algebra
This paper investigates Y(z)-injective vertex superalgebras. We first establish that two fundamental classes of vertex superalgebras -- simple ones and those admitting a PBW basis -- are Y(z)-injective. We then study actions of Hopf algebras on Y(z)-injective vertex superalgebras and prove that every finite-dimensional Hopf algebra acting inner faithfully on such algebras must be a group algebra. As a direct consequence, the study of the structure and representation theory of fixed-point subalgebras under finite-dimensional Hopf algebra actions reduces to that under group actions.
title Y(z)-injective vertex superalgebras and Hopf actions
topic Quantum Algebra
url https://arxiv.org/abs/2509.03989