The Ribbon Elements of Drinfeld Double of Radford Hopf Algebra
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911993798066176 |
|---|---|
| author | Sun, Hua Zhang, Yuyan Li, Libin |
| author_facet | Sun, Hua Zhang, Yuyan Li, Libin |
| contents | Let $m$, $n$ be two positive integers, $\Bbbk$ be an algebraically closed field with char($\Bbbk)\nmid mn$. Radford constructed an $mn^{2}$-dimensional Hopf algebra $R_{mn}(q)$ such that its Jacobson radical is not a Hopf ideal. We show that the Drinfeld double $D(R_{mn}(q))$ of Radford Hopf algebra $R_{mn}(q)$ has ribbon elements if and only if $n$ is odd. Moreover, if $m$ is even and $n$ is odd, then $D(R_{mn}(q))$ has two ribbon elements, if both $m$ and $n$ are odd, then $D(R_{mn}(q))$ has only one ribbon element. Finally, we compute explicitly all ribbon elements of $D(R_{mn}(q))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Ribbon Elements of Drinfeld Double of Radford Hopf Algebra Sun, Hua Zhang, Yuyan Li, Libin Quantum Algebra Let $m$, $n$ be two positive integers, $\Bbbk$ be an algebraically closed field with char($\Bbbk)\nmid mn$. Radford constructed an $mn^{2}$-dimensional Hopf algebra $R_{mn}(q)$ such that its Jacobson radical is not a Hopf ideal. We show that the Drinfeld double $D(R_{mn}(q))$ of Radford Hopf algebra $R_{mn}(q)$ has ribbon elements if and only if $n$ is odd. Moreover, if $m$ is even and $n$ is odd, then $D(R_{mn}(q))$ has two ribbon elements, if both $m$ and $n$ are odd, then $D(R_{mn}(q))$ has only one ribbon element. Finally, we compute explicitly all ribbon elements of $D(R_{mn}(q))$. |
| title | The Ribbon Elements of Drinfeld Double of Radford Hopf Algebra |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2408.09737 |