On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914892746850304 |
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| author | De Renzi, Marco Martel, Jules |
| author_facet | De Renzi, Marco Martel, Jules |
| contents | For a root of unity $ζ$ of odd prime order, we restrict coefficients of non-semisimple quantum representations of mapping class groups associated with the small quantum group $\mathfrak{u}_ζ\mathfrak{sl}_2$ from $\mathbb{Q}(ζ)$ to $\mathbb{Z}[ζ]$. We do this by exhibiting explicit bases of states spaces that span $\mathbb{Z}[ζ]$-lattices that are invariant under projective actions of mapping class groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20644 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups De Renzi, Marco Martel, Jules Geometric Topology Quantum Algebra For a root of unity $ζ$ of odd prime order, we restrict coefficients of non-semisimple quantum representations of mapping class groups associated with the small quantum group $\mathfrak{u}_ζ\mathfrak{sl}_2$ from $\mathbb{Q}(ζ)$ to $\mathbb{Z}[ζ]$. We do this by exhibiting explicit bases of states spaces that span $\mathbb{Z}[ζ]$-lattices that are invariant under projective actions of mapping class groups. |
| title | On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups |
| topic | Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2407.20644 |