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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.15909 |
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| _version_ | 1866914569146859520 |
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| author | Anić, Jelena Felder, Giovanni |
| author_facet | Anić, Jelena Felder, Giovanni |
| contents | We introduce the notion of $π^2$-graded Hopf algebra, where the grading is by the double groupoid of commutative diagrams of a finite groupoid $π$. The finite dimensional representations of a $π^2$-graded Hopf algebra form a rigid monoidal category with a fibre functor to the category of $π$-graded vector spaces. The main example is given by the restricted quantum groups underlying the Andrews-Baxter-Forrester restricted solid-on-solid models of statistical mechanics and, more generally, the Jimbo-Miwa-Okado models associated to classical Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15909 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Restricted quantum groups as graded Hopf algebras Anić, Jelena Felder, Giovanni Quantum Algebra Representation Theory 16T05, 17B37, 18M15 We introduce the notion of $π^2$-graded Hopf algebra, where the grading is by the double groupoid of commutative diagrams of a finite groupoid $π$. The finite dimensional representations of a $π^2$-graded Hopf algebra form a rigid monoidal category with a fibre functor to the category of $π$-graded vector spaces. The main example is given by the restricted quantum groups underlying the Andrews-Baxter-Forrester restricted solid-on-solid models of statistical mechanics and, more generally, the Jimbo-Miwa-Okado models associated to classical Lie algebras. |
| title | Restricted quantum groups as graded Hopf algebras |
| topic | Quantum Algebra Representation Theory 16T05, 17B37, 18M15 |
| url | https://arxiv.org/abs/2605.15909 |