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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12201 |
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| _version_ | 1866917792560709632 |
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| author | Huang, Hongdi Nguyen, Van C. Veerapen, Padmini Vashaw, Kent B. Wang, Xingting |
| author_facet | Huang, Hongdi Nguyen, Van C. Veerapen, Padmini Vashaw, Kent B. Wang, Xingting |
| contents | We show that if two $m$-homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalence between the categories of comodules for their associated universal quantum groups (in the sense of Manin) which sends one algebra to the other. As a consequence, any Zhang twist of an $m$-homogeneous algebra is a 2-cocycle twist by some 2-cocycle from its Manin's universal quantum group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-symmetric equivalence is a graded Morita invariant Huang, Hongdi Nguyen, Van C. Veerapen, Padmini Vashaw, Kent B. Wang, Xingting Quantum Algebra Rings and Algebras 16T05, 16W50, 17B37 We show that if two $m$-homogeneous algebras have Morita equivalent graded module categories, then they are quantum-symmetrically equivalent, that is, there is a monoidal equivalence between the categories of comodules for their associated universal quantum groups (in the sense of Manin) which sends one algebra to the other. As a consequence, any Zhang twist of an $m$-homogeneous algebra is a 2-cocycle twist by some 2-cocycle from its Manin's universal quantum group. |
| title | Quantum-symmetric equivalence is a graded Morita invariant |
| topic | Quantum Algebra Rings and Algebras 16T05, 16W50, 17B37 |
| url | https://arxiv.org/abs/2405.12201 |