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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.03989 |
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Table of 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.