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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2503.02035 |
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| _version_ | 1866917944547606528 |
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| author | Ryom-Hansen, Steen |
| author_facet | Ryom-Hansen, Steen |
| contents | We consider the bt-algebra ${ \mathcal E}_n(q)$ of knot theory, defined over an arbitrary field $ \Bbbk$. We find a KLR-like presentation for $ {\mathcal E}_n(q) $ showing that it is a $ \mathbb Z$-graded algebra if $ q \in \Bbbk^{\times} \setminus \{1 \} $ admits a square root in $ \Bbbk $. We introduce the ordered bt-algebra $ {\mathcal E}^{\rm{ord}}_n(q)$ and show that it also has a KLR-like presentation, without restriction on $ q \in \Bbbk^{\times} \setminus \{1 \} $. In particular, $ {\mathcal E}^{\rm{ord}}_n(q)$ is a $ \mathbb Z$-graded algebra for all $ q \in \Bbbk^{\times} \setminus \{1 \} $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A KLR-like presentation for the bt-algebra Ryom-Hansen, Steen Representation Theory We consider the bt-algebra ${ \mathcal E}_n(q)$ of knot theory, defined over an arbitrary field $ \Bbbk$. We find a KLR-like presentation for $ {\mathcal E}_n(q) $ showing that it is a $ \mathbb Z$-graded algebra if $ q \in \Bbbk^{\times} \setminus \{1 \} $ admits a square root in $ \Bbbk $. We introduce the ordered bt-algebra $ {\mathcal E}^{\rm{ord}}_n(q)$ and show that it also has a KLR-like presentation, without restriction on $ q \in \Bbbk^{\times} \setminus \{1 \} $. In particular, $ {\mathcal E}^{\rm{ord}}_n(q)$ is a $ \mathbb Z$-graded algebra for all $ q \in \Bbbk^{\times} \setminus \{1 \} $. |
| title | A KLR-like presentation for the bt-algebra |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2503.02035 |