Ribbon categories from ind-exact algebras: simple current case
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911553438089216 |
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| author | Shimizu, Kenichi Yadav, Harshit |
| author_facet | Shimizu, Kenichi Yadav, Harshit |
| contents | We give criteria for when finitely generated local modules over a commutative algebra $A$ in the ind-completion $\widehat{\mathcal{C}}$ of a braided tensor category $\mathcal{C}$ inherit the structure of a (rigid, braided, ribbon) tensor category. We then apply this to simple current algebras $A = \bigoplus_{g \in Γ} E_g$, where $Γ$ is a subgroup of invertible objects in $\mathcal{C}$. Using a description of simple $A$-modules, we verify the required hypotheses for this class of algebras and deduce rigidity, braided, ribbon, and non-degeneracy properties for their finitely generated local modules. As applications, we construct examples of ribbon tensor categories from quantum supergroup categories for unrolled $\mathfrak{gl}(1|1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28215 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ribbon categories from ind-exact algebras: simple current case Shimizu, Kenichi Yadav, Harshit Quantum Algebra Category Theory Representation Theory We give criteria for when finitely generated local modules over a commutative algebra $A$ in the ind-completion $\widehat{\mathcal{C}}$ of a braided tensor category $\mathcal{C}$ inherit the structure of a (rigid, braided, ribbon) tensor category. We then apply this to simple current algebras $A = \bigoplus_{g \in Γ} E_g$, where $Γ$ is a subgroup of invertible objects in $\mathcal{C}$. Using a description of simple $A$-modules, we verify the required hypotheses for this class of algebras and deduce rigidity, braided, ribbon, and non-degeneracy properties for their finitely generated local modules. As applications, we construct examples of ribbon tensor categories from quantum supergroup categories for unrolled $\mathfrak{gl}(1|1)$. |
| title | Ribbon categories from ind-exact algebras: simple current case |
| topic | Quantum Algebra Category Theory Representation Theory |
| url | https://arxiv.org/abs/2603.28215 |