Quantum Heisenberg Enveloping Algebra
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929235145261056 |
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| author | Bera, Sanu Mandal, Sugata Nandy, Soumendu |
| author_facet | Bera, Sanu Mandal, Sugata Nandy, Soumendu |
| contents | In this article, the two-parameter quantum Heisenberg enveloping algebra, which serves as a model for certain quantum generalized Heisenberg algebras, have been studied at roots of unity. In this context, the quantum Heisenberg enveloping algebra becomes a polynomial identity algebra, and the dimension of simple modules is bounded by its PI degree. The PI degree, center, and complete classification of simple modules up to isomorphism are explicitly presented. We work over a field of arbitrary characteristic, although our results concerning the representations require that it is algebraically closed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Heisenberg Enveloping Algebra Bera, Sanu Mandal, Sugata Nandy, Soumendu Representation Theory Quantum Algebra Rings and Algebras In this article, the two-parameter quantum Heisenberg enveloping algebra, which serves as a model for certain quantum generalized Heisenberg algebras, have been studied at roots of unity. In this context, the quantum Heisenberg enveloping algebra becomes a polynomial identity algebra, and the dimension of simple modules is bounded by its PI degree. The PI degree, center, and complete classification of simple modules up to isomorphism are explicitly presented. We work over a field of arbitrary characteristic, although our results concerning the representations require that it is algebraically closed. |
| title | Quantum Heisenberg Enveloping Algebra |
| topic | Representation Theory Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2402.03793 |