Derivations and Hochschild cohomology of quantum nilpotent algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908356539580416 |
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| author | Launois, Stéphane Lopes, Samuel A. Oppong, Isaac |
| author_facet | Launois, Stéphane Lopes, Samuel A. Oppong, Isaac |
| contents | We compute the derivations of Quantum Nilpotent Algebras under a technical (but necessary) assumption on the center. As a consequence, we give an explicit description of the first Hochschild cohomology group of $U_q^+(\mathfrak{g})$, the positive part of the quantized enveloping algebra of a finite-dimensional complex simple Lie algebra $\mathfrak{g}$. Our results are obtained leveraging an initial cluster constructed by Goodearl and Yakimov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivations and Hochschild cohomology of quantum nilpotent algebras Launois, Stéphane Lopes, Samuel A. Oppong, Isaac Quantum Algebra Rings and Algebras We compute the derivations of Quantum Nilpotent Algebras under a technical (but necessary) assumption on the center. As a consequence, we give an explicit description of the first Hochschild cohomology group of $U_q^+(\mathfrak{g})$, the positive part of the quantized enveloping algebra of a finite-dimensional complex simple Lie algebra $\mathfrak{g}$. Our results are obtained leveraging an initial cluster constructed by Goodearl and Yakimov. |
| title | Derivations and Hochschild cohomology of quantum nilpotent algebras |
| topic | Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2505.06205 |