Regular actions and semisimplicity of conformal modules over the general conformal algebra
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915592148090880 |
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| author | Su, Yucai Xia, Chunguang |
| author_facet | Su, Yucai Xia, Chunguang |
| contents | We introduce the notion of a regular action in the category of conformal modules over Lie conformal algebras with Virasoro elements. We show that a finite conformal module over the general conformal algebra $\mathfrak{gc}_1$ (resp., $\mathfrak{gc}_N$ with $N\ge2$) is semisimple if and only if there exists a pair of different Virasoro elements (resp., canonical Virasoro elements) with regular actions. Along the way to finding a semisimplicity criteria, we also discuss the classification of Virasoro elements of $\mathfrak{gc}_N$ in-depth, leading us to construct a huge number of new Virasoro conformal modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular actions and semisimplicity of conformal modules over the general conformal algebra Su, Yucai Xia, Chunguang Representation Theory Mathematical Physics Rings and Algebras We introduce the notion of a regular action in the category of conformal modules over Lie conformal algebras with Virasoro elements. We show that a finite conformal module over the general conformal algebra $\mathfrak{gc}_1$ (resp., $\mathfrak{gc}_N$ with $N\ge2$) is semisimple if and only if there exists a pair of different Virasoro elements (resp., canonical Virasoro elements) with regular actions. Along the way to finding a semisimplicity criteria, we also discuss the classification of Virasoro elements of $\mathfrak{gc}_N$ in-depth, leading us to construct a huge number of new Virasoro conformal modules. |
| title | Regular actions and semisimplicity of conformal modules over the general conformal algebra |
| topic | Representation Theory Mathematical Physics Rings and Algebras |
| url | https://arxiv.org/abs/2511.00666 |