Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.04125 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910861382123520 |
|---|---|
| author | Chen, Jiayi Ruan, Shiquan |
| author_facet | Chen, Jiayi Ruan, Shiquan |
| contents | Motivated by the construction of $\imath$Hall algebras and $Δ$-Hall algebras, we introduce $\imath$Hopf algebras associated with symmetrically self-dual Hopf algebras. We prove that the $\imath$Hopf algebra is an associative algebra with a unit, where the associativity relies on an analogue of Green's formula in the framework of Hopf algebras. As an application, we construct the $\imath$Taft algebra of dimension 4, which is proved to be isomorphic to the group algebra of $\mathbb{Z}/4\mathbb{Z}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04125 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\imath$Hopf algebras associated with self-dual Hopf algebras Chen, Jiayi Ruan, Shiquan Rings and Algebras 16T05, 16T20 Motivated by the construction of $\imath$Hall algebras and $Δ$-Hall algebras, we introduce $\imath$Hopf algebras associated with symmetrically self-dual Hopf algebras. We prove that the $\imath$Hopf algebra is an associative algebra with a unit, where the associativity relies on an analogue of Green's formula in the framework of Hopf algebras. As an application, we construct the $\imath$Taft algebra of dimension 4, which is proved to be isomorphic to the group algebra of $\mathbb{Z}/4\mathbb{Z}$. |
| title | $\imath$Hopf algebras associated with self-dual Hopf algebras |
| topic | Rings and Algebras 16T05, 16T20 |
| url | https://arxiv.org/abs/2503.04125 |