Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1801.07524 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916141396393984 |
|---|---|
| author | Faitg, Matthieu |
| author_facet | Faitg, Matthieu |
| contents | We prove two results about $\text{SLF}(\bar U_q)$, the algebra of symmetric linear forms on the restricted quantum group $\bar U_q = \bar U_q(\mathfrak{sl}(2))$. First, we express any trace on finite dimensional projective $\bar U_q$-modules as a linear combination in the basis of $\text{SLF}(\bar U_q)$ constructed by Gainutdinov - Tipunin and also by Arike. In particular, this allows us to determine the symmetric linear form corresponding to the modified trace on projective $\bar U_q$-modules. Second, we give the explicit multiplication rules between symmetric linear forms in this basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_07524 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A note on symmetric linear forms and traces on the restricted quantum group $\bar U_q(\mathfrak{sl}(2))$ Faitg, Matthieu Quantum Algebra We prove two results about $\text{SLF}(\bar U_q)$, the algebra of symmetric linear forms on the restricted quantum group $\bar U_q = \bar U_q(\mathfrak{sl}(2))$. First, we express any trace on finite dimensional projective $\bar U_q$-modules as a linear combination in the basis of $\text{SLF}(\bar U_q)$ constructed by Gainutdinov - Tipunin and also by Arike. In particular, this allows us to determine the symmetric linear form corresponding to the modified trace on projective $\bar U_q$-modules. Second, we give the explicit multiplication rules between symmetric linear forms in this basis. |
| title | A note on symmetric linear forms and traces on the restricted quantum group $\bar U_q(\mathfrak{sl}(2))$ |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/1801.07524 |