Calabi–Yau property of quantum groups of GL(2) representation type

DOI10.1142/s0219498824501044zbMath1530.16036arXiv2303.14051MaRDI QIDQ6104134

Xiao Lan Yu, Xingting Wang

Publication date: 28 June 2023

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.14051

zbMATH Keywords

quantum groupCalabi-Yau algebracogroupoid

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Homological conditions on associative rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.) (16E65) Hopf algebras and their applications (16T05)

Cites Work

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• Skew Calabi-Yau algebras and homological identities.
• Dualising complexes and twisted Hochschild (co)homology for Noetherian Hopf algebras.
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• Calabi-Yau property under monoidal Morita-Takeuchi equivalence
• Quantum groups of \(\mathrm{GL}(2)\) representation type.
• The quantum group of a nondegenerate bilinear form.
• Hopf–Galois objects of Calabi–Yau Hopf algebras
• Bialgebra cohomology, deformations, and quantum groups.
• Hopf bigalois extensions
• Hochschild homology of Hopf algebras and free Yetter–Drinfeld resolutions of the counit
• Hopf-Galois objects and cogroupoids

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