Y(z)-injective vertex superalgebras and Hopf actions
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908519005945856 |
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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 |