Derivations and Hochschild cohomology of quantum nilpotent algebras

2025/05/09 by Launois, Stéphane, Lopes, Samuel A., Oppong, Isaac · 1 citation
#FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2505.06205

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⁺(\mathfrakg), the positive part of the quantized enveloping algebra of a finite-dimensional complex simple Lie algebra \mathfrakg. Our results are obtained leveraging an initial cluster constructed by Goodearl and Yakimov.

Citations

• Enveloping algebras of derivations of commutative and noncommutative algebras
• Derivations of the Positive Part of the Two-parameter Quantum Group of type G₂
• The Berenstein-Zelevinsky quantum cluster algebra conjecture
• Unipotent and Nakayama automorphisms of quantum nilpotent algebras
• From quantum Ore extensions to quantum tori via noncommutative UFDs
• On the cohomology of the Weyl algebra, the quantum plane, and the q-Weyl algebra
• Rigidity of quantum tori and the Andruskiewitsch-Dumas conjecture
• On the Spectra of Quantum Groups
• Derivations of the two-parameter quantized enveloping algebra \U
• Cauchon diagrams for quantized enveloping algebras
• The first Hochschild cohomology group of quantum matrices and the quantum special linear group
• Quantum unique factorisation domains

Cited by

• Quantum upper triangular matrix algebras

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• Derivations of the Positive Part of the Two-parameter Quantum Group of type G₂
• The first Hochschild cohomology group of quantum matrices and the quantum special linear group
• Derivations and the first Hochschild cohomology group of the quantum grassmannian
• Quantum upper triangular matrix algebras