The quantum torus as an $\mathbb E_M$-category
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914167451025408 |
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| author | Chen, Lin Zhao, Yifei |
| author_facet | Chen, Lin Zhao, Yifei |
| contents | Given an oriented $2$-manifold $M$, a locally constant sheaf of lattices $Λ$ over $M$, and a pointed morphism $q : \textsf B^2Λ\rightarrow \textsf B^4\mathbf C^{\times}$, we define an $\mathbb E_M$-category $\mathrm{Rep}_q(\check T)$ which we call the "quantum torus" at level $q$. We explain why this terminology is deserved and calculate the factorization homology of $\mathrm{Rep}_q(\check T)$. When $M$ arises from a global complex curve, we confirm (a version of) a conjecture of Ben-Zvi and Nadler for tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantum torus as an $\mathbb E_M$-category Chen, Lin Zhao, Yifei Representation Theory Quantum Algebra 18M15 Given an oriented $2$-manifold $M$, a locally constant sheaf of lattices $Λ$ over $M$, and a pointed morphism $q : \textsf B^2Λ\rightarrow \textsf B^4\mathbf C^{\times}$, we define an $\mathbb E_M$-category $\mathrm{Rep}_q(\check T)$ which we call the "quantum torus" at level $q$. We explain why this terminology is deserved and calculate the factorization homology of $\mathrm{Rep}_q(\check T)$. When $M$ arises from a global complex curve, we confirm (a version of) a conjecture of Ben-Zvi and Nadler for tori. |
| title | The quantum torus as an $\mathbb E_M$-category |
| topic | Representation Theory Quantum Algebra 18M15 |
| url | https://arxiv.org/abs/2511.18113 |