Quasi-Hopf Algebras of Dimension 6
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909336375132160 |
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| author | Bulacu, Daniel Misurati, Matteo |
| author_facet | Bulacu, Daniel Misurati, Matteo |
| contents | We complete the classification of the 6-dimensional quasi-Hopf algebras, by proving that any such algebra is semisimple. As byproducts, we provide examples of 6-dimensional quasi-bialgebras that are not semisimple as algebras, as well as the concrete quasi-Hopf structures of the 6-dimensional semisimple quasi-Hopf algebras previously classified by Etingof and Gelaki in terms of their category of representations. In total there are 15 quasi-Hopf algebras in dimension 6 which are not pairwise twist equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-Hopf Algebras of Dimension 6 Bulacu, Daniel Misurati, Matteo Quantum Algebra 16W30 We complete the classification of the 6-dimensional quasi-Hopf algebras, by proving that any such algebra is semisimple. As byproducts, we provide examples of 6-dimensional quasi-bialgebras that are not semisimple as algebras, as well as the concrete quasi-Hopf structures of the 6-dimensional semisimple quasi-Hopf algebras previously classified by Etingof and Gelaki in terms of their category of representations. In total there are 15 quasi-Hopf algebras in dimension 6 which are not pairwise twist equivalent. |
| title | Quasi-Hopf Algebras of Dimension 6 |
| topic | Quantum Algebra 16W30 |
| url | https://arxiv.org/abs/2410.03476 |