On bicrossed modules of Hopf algebras
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915398706790400 |
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| author | Han, Xiao |
| author_facet | Han, Xiao |
| contents | We use Hopf algebroids to formulate a notion of a noncommutative and non-cocommutative Hopf 2-algebra. We show how these arise from a bicrossproduct Hopf algebra with Peiffer identities. In particular, we show that for a Hopf algebra $H$ with bijective antipode, the mirror bicrossproduct Hopf algebra $H\triangleright\!\!\!\blacktriangleleft H_{cop}$ is a Hopf 2-algebra. We apply the theorem on Sweedler's Hopf algebra as an example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10173 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On bicrossed modules of Hopf algebras Han, Xiao Quantum Algebra 16T05, 20G42 We use Hopf algebroids to formulate a notion of a noncommutative and non-cocommutative Hopf 2-algebra. We show how these arise from a bicrossproduct Hopf algebra with Peiffer identities. In particular, we show that for a Hopf algebra $H$ with bijective antipode, the mirror bicrossproduct Hopf algebra $H\triangleright\!\!\!\blacktriangleleft H_{cop}$ is a Hopf 2-algebra. We apply the theorem on Sweedler's Hopf algebra as an example. |
| title | On bicrossed modules of Hopf algebras |
| topic | Quantum Algebra 16T05, 20G42 |
| url | https://arxiv.org/abs/2312.10173 |