Simple Modules over Second Quantum Weyl Algebra
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929644643549184 |
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| author | Bera, Sanu |
| author_facet | Bera, Sanu |
| contents | In this article, we study the multiparameter second quantum Weyl algebra at roots of unity. In this setting, the algebra is a polynomial identity (PI) algebra, and the dimension of its simple modules is bounded above by its PI degree. We explicitly determine the PI degree and provide a complete classification of simple modules. This classification offers a comprehensive solution to $\href{https://doi.org/10.1007/978-3-030-19486-4_23}{\text{Problem 2: C, Walton (2019)- An Invitation to Noncommutative Algebra}}$ for the second quantum Weyl algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple Modules over Second Quantum Weyl Algebra Bera, Sanu Representation Theory Quantum Algebra 16D60, 16D70, 16S36, 16R20, 16T20 In this article, we study the multiparameter second quantum Weyl algebra at roots of unity. In this setting, the algebra is a polynomial identity (PI) algebra, and the dimension of its simple modules is bounded above by its PI degree. We explicitly determine the PI degree and provide a complete classification of simple modules. This classification offers a comprehensive solution to $\href{https://doi.org/10.1007/978-3-030-19486-4_23}{\text{Problem 2: C, Walton (2019)- An Invitation to Noncommutative Algebra}}$ for the second quantum Weyl algebra. |
| title | Simple Modules over Second Quantum Weyl Algebra |
| topic | Representation Theory Quantum Algebra 16D60, 16D70, 16S36, 16R20, 16T20 |
| url | https://arxiv.org/abs/2412.17261 |