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arXiv · 2505.06205

Derivations and Hochschild cohomology of quantum nilpotent algebras

Stéphane Launois·Samuel A. Lopes·Isaac Oppong
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Abstract

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.

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Stéphane Launois, Samuel A. Lopes, Isaac Oppong. 2025-05-09. Derivations and Hochschild cohomology of quantum nilpotent algebras. https://arxiv.org/abs/2505.06205

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