A Quasi-Pentagon Equation for a Heisenberg Double of a Quasi-Hopf Algebra
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915936522469376 |
|---|---|
| author | Ota, Yohei |
| author_facet | Ota, Yohei |
| contents | For a finite-dimensional Hopf algebra $H$, the canonical elements of the Heisenberg doubles $\mathcal{H}(H^\ast)$ and $\mathcal{H}(H)$ satisfy the pentagon and Hopf equations, respectively. In this paper we construct quasi-Hopf analogues of these structures. For a finite-dimensional quasi-Hopf algebra $H$, we consider natural quasi-Hopf analogues $\mathcal{H}_1(H^\ast)$ and $\mathcal{H}_1(H)$ of $\mathcal{H}(H^\ast)$ and $\mathcal{H}(H)$. Although their canonical elements are defined just as in the Hopf algebra case, they need not be invertible. We prove that there nevertheless exist natural inverse-like elements. In $\mathcal{H}_1(H^\ast)$, the canonical element satisfies a quasi-pentagon equation and its inverse-like element satisfies a quasi-Hopf equation, while in $\mathcal{H}_1(H)$ the roles are reversed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12554 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Quasi-Pentagon Equation for a Heisenberg Double of a Quasi-Hopf Algebra Ota, Yohei Quantum Algebra For a finite-dimensional Hopf algebra $H$, the canonical elements of the Heisenberg doubles $\mathcal{H}(H^\ast)$ and $\mathcal{H}(H)$ satisfy the pentagon and Hopf equations, respectively. In this paper we construct quasi-Hopf analogues of these structures. For a finite-dimensional quasi-Hopf algebra $H$, we consider natural quasi-Hopf analogues $\mathcal{H}_1(H^\ast)$ and $\mathcal{H}_1(H)$ of $\mathcal{H}(H^\ast)$ and $\mathcal{H}(H)$. Although their canonical elements are defined just as in the Hopf algebra case, they need not be invertible. We prove that there nevertheless exist natural inverse-like elements. In $\mathcal{H}_1(H^\ast)$, the canonical element satisfies a quasi-pentagon equation and its inverse-like element satisfies a quasi-Hopf equation, while in $\mathcal{H}_1(H)$ the roles are reversed. |
| title | A Quasi-Pentagon Equation for a Heisenberg Double of a Quasi-Hopf Algebra |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2604.12554 |