Rank-two parabolic-type VOAs and nilpotency of nil ideals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913100077203456 |
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| author | Liu, Jianqi |
| author_facet | Liu, Jianqi |
| contents | In this paper, we undertake a systematic study of the parabolic-type sub-vertex operator algebras (subVOAs) \(V_P\) of rank-two lattice VOAs \(V_L\), originally introduced by the first-named author. We first classify all possible types of such subVOAs by analyzing the corresponding submonoids \(P \subseteq L\). For each type of \(V_P\), we then classify its irreducible modules. Certain Zhu algebras \(A(V_P)\) provide new examples of rings with nil ideals that are not nilpotent. Finally, we show that the simple quotient \(V_H\) of any parabolic-type subVOA \(V_P\) is a \(C_1\)-cofinite irrational VOA satisfying the strongly unital property recently introduced by Damiolini--Gibney--Krashen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21662 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rank-two parabolic-type VOAs and nilpotency of nil ideals Liu, Jianqi Quantum Algebra In this paper, we undertake a systematic study of the parabolic-type sub-vertex operator algebras (subVOAs) \(V_P\) of rank-two lattice VOAs \(V_L\), originally introduced by the first-named author. We first classify all possible types of such subVOAs by analyzing the corresponding submonoids \(P \subseteq L\). For each type of \(V_P\), we then classify its irreducible modules. Certain Zhu algebras \(A(V_P)\) provide new examples of rings with nil ideals that are not nilpotent. Finally, we show that the simple quotient \(V_H\) of any parabolic-type subVOA \(V_P\) is a \(C_1\)-cofinite irrational VOA satisfying the strongly unital property recently introduced by Damiolini--Gibney--Krashen. |
| title | Rank-two parabolic-type VOAs and nilpotency of nil ideals |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2508.21662 |