Zhu algebras of superconformal vertex algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914447177547776 |
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| author | Sato, Ryo Yanagida, Shintarou |
| author_facet | Sato, Ryo Yanagida, Shintarou |
| contents | The purpose of this note is to demonstrate the advantages of Y.-Z.~Huang's definition of the Zhu algebra
(Comm.\ Contemp.\ Math., 7 (2005), no.~5, 649--706) for an arbitrary vertex algebra, not necessarily equipped with a Hamiltonian operator or a Virasoro element, by achieving the following two goals: (1) determining the Zhu algebras of $N=1, 2, 3, 4$ and big $N=4$ superconformal vertex algebras, and (2) introducing the Zhu algebras of $N_K=N$ supersymmetric vertex algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zhu algebras of superconformal vertex algebras Sato, Ryo Yanagida, Shintarou Quantum Algebra Representation Theory The purpose of this note is to demonstrate the advantages of Y.-Z.~Huang's definition of the Zhu algebra (Comm.\ Contemp.\ Math., 7 (2005), no.~5, 649--706) for an arbitrary vertex algebra, not necessarily equipped with a Hamiltonian operator or a Virasoro element, by achieving the following two goals: (1) determining the Zhu algebras of $N=1, 2, 3, 4$ and big $N=4$ superconformal vertex algebras, and (2) introducing the Zhu algebras of $N_K=N$ supersymmetric vertex algebras. |
| title | Zhu algebras of superconformal vertex algebras |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2509.13124 |