Borel-type subalgebras of the lattice vertex operator algebra
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912377114460160 |
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| author | Liu, Jianqi |
| author_facet | Liu, Jianqi |
| contents | In this paper, we introduce and study new classes of sub-vertex operator algebras of the lattice vertex operator algebras (VOAs), which we call the conic, Borel, and parabolic-type subVOAs. These CFT-type VOAs, which are not necessarily strongly finitely generated, satisfy properties similar to the usual Borel and parabolic subalgebras of a Lie algebra. For the lowest-rank nontrivial example of Borel-type subVOA $V_{B}$ of $V_{\Z\al}$, we explicitly determine its Zhu's algebra $A(V_B)$ in terms of generators and relations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02278 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Borel-type subalgebras of the lattice vertex operator algebra Liu, Jianqi Quantum Algebra Representation Theory In this paper, we introduce and study new classes of sub-vertex operator algebras of the lattice vertex operator algebras (VOAs), which we call the conic, Borel, and parabolic-type subVOAs. These CFT-type VOAs, which are not necessarily strongly finitely generated, satisfy properties similar to the usual Borel and parabolic subalgebras of a Lie algebra. For the lowest-rank nontrivial example of Borel-type subVOA $V_{B}$ of $V_{\Z\al}$, we explicitly determine its Zhu's algebra $A(V_B)$ in terms of generators and relations. |
| title | Borel-type subalgebras of the lattice vertex operator algebra |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2402.02278 |