Presentations for small reflection equation algebras of type A
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918056055275520 |
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| author | Cooke, Juliet Laugwitz, Robert |
| author_facet | Cooke, Juliet Laugwitz, Robert |
| contents | We give presentations, in terms of the generators and relations, for the reflection equation algebras of type $GL_n$ and $SL_n$, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of $\mathfrak{gl}_n$ and $\mathfrak{sl}_n$. Our presentations display these algebras as quotients of the infinite-dimensional reflection equation algebras of types $GL_n$ and $SL_n$ by identifying additional relations that correspond to twisting the nilpotency and unipotency relations of the finite-dimensional quantum function algebras. The presentations are valid for appropriately defined integral forms of these algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16004 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Presentations for small reflection equation algebras of type A Cooke, Juliet Laugwitz, Robert Quantum Algebra Category Theory Rings and Algebras 17B37 (Primary) 16T05, 18M05, 18M15 (Secondary) We give presentations, in terms of the generators and relations, for the reflection equation algebras of type $GL_n$ and $SL_n$, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of $\mathfrak{gl}_n$ and $\mathfrak{sl}_n$. Our presentations display these algebras as quotients of the infinite-dimensional reflection equation algebras of types $GL_n$ and $SL_n$ by identifying additional relations that correspond to twisting the nilpotency and unipotency relations of the finite-dimensional quantum function algebras. The presentations are valid for appropriately defined integral forms of these algebras. |
| title | Presentations for small reflection equation algebras of type A |
| topic | Quantum Algebra Category Theory Rings and Algebras 17B37 (Primary) 16T05, 18M05, 18M15 (Secondary) |
| url | https://arxiv.org/abs/2412.16004 |