Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2011.02463 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929466759970816 |
|---|---|
| author | Terwilliger, Paul |
| author_facet | Terwilliger, Paul |
| contents | This paper concerns the positive part $U^+_q$ of the quantum group $U_q({\widehat{\mathfrak{sl}}}_2)$. The algebra $U^+_q$ has a presentation involving two generators that satisfy the cubic $q$-Serre relations. We recently introduced an algebra $\mathcal U^+_q$ called the alternating central extension of $U^+_q$. We presented $\mathcal U^+_q$ by generators and relations. The presentation is attractive, but the multitude of generators and relations makes the presentation unwieldy. In this paper we obtain a presentation of $\mathcal U^+_q$ that involves a small subset of the original set of generators and a very manageable set of relations. We call this presentation the compact presentation of $\mathcal U^+_q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_02463 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A compact presentation for the alternating central extension of the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$ Terwilliger, Paul Quantum Algebra Combinatorics 17B37 This paper concerns the positive part $U^+_q$ of the quantum group $U_q({\widehat{\mathfrak{sl}}}_2)$. The algebra $U^+_q$ has a presentation involving two generators that satisfy the cubic $q$-Serre relations. We recently introduced an algebra $\mathcal U^+_q$ called the alternating central extension of $U^+_q$. We presented $\mathcal U^+_q$ by generators and relations. The presentation is attractive, but the multitude of generators and relations makes the presentation unwieldy. In this paper we obtain a presentation of $\mathcal U^+_q$ that involves a small subset of the original set of generators and a very manageable set of relations. We call this presentation the compact presentation of $\mathcal U^+_q$. |
| title | A compact presentation for the alternating central extension of the positive part of $U_q(\widehat{\mathfrak{sl}}_2)$ |
| topic | Quantum Algebra Combinatorics 17B37 |
| url | https://arxiv.org/abs/2011.02463 |