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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.21170 |
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| _version_ | 1866917968792780800 |
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| author | Bera, Sanu Mukherjee, Snehashis |
| author_facet | Bera, Sanu Mukherjee, Snehashis |
| contents | In this article we investigate the algebra $U_q^+(B_2)$. Assume that $q$ is a primitive $m$-th root of unity with $m \geq 5$. We prove that $U_q^+(B_2)$ becomes a Polynomial Identity (PI) algebra. It was previously known that for such algebras the simple modules are finite-dimensional with dimension at most the PI degree. We determine the PI degree of $U_q^+(B_2)$ and we classify up to isomorphism the simple $U_q^+(B_2)$-modules. We also find the center of $U_q^+(B_2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $U_q^+(B_2)$ and its representations Bera, Sanu Mukherjee, Snehashis Representation Theory In this article we investigate the algebra $U_q^+(B_2)$. Assume that $q$ is a primitive $m$-th root of unity with $m \geq 5$. We prove that $U_q^+(B_2)$ becomes a Polynomial Identity (PI) algebra. It was previously known that for such algebras the simple modules are finite-dimensional with dimension at most the PI degree. We determine the PI degree of $U_q^+(B_2)$ and we classify up to isomorphism the simple $U_q^+(B_2)$-modules. We also find the center of $U_q^+(B_2)$. |
| title | $U_q^+(B_2)$ and its representations |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2503.21170 |