Hochschild homology of Hopf algebras and free Yetter–Drinfeld resolutions of the counit

DOI10.1112/S0010437X12000656zbMath1365.16016arXiv1204.0687OpenAlexW3100579360MaRDI QIDQ4923466

Julien Bichon

Publication date: 24 May 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.0687

zbMATH Keywords

Hochschild homologyHopf algebraYetter-Drinfeld module\(L^2\)-Betti numbers

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) Hopf algebras and their applications (16T05)

Related Items (15)

The diffeomorphism group of the solid closed torus and Hochschild homology ⋮ On the monoidal invariance of the cohomological dimension of Hopf algebras ⋮ On quantum groups associated to non-Noetherian regular algebras of dimension 2 ⋮ Lévy–Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups ⋮ Calabi-Yau property under monoidal Morita-Takeuchi equivalence ⋮ \(L^2\)-Betti numbers of rigid \(C^\ast\)-tensor categories and discrete quantum groups ⋮ Second cohomology groups of the Hopf\(^*\)-algebras associated to universal unitary quantum groups ⋮ The differential graded Verlinde formula and the Deligne Conjecture ⋮ Calabi–Yau property of quantum groups of GL(2) representation type ⋮ Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras ⋮ Note on the Hochschild cohomology of Hopf-Galois extension ⋮ Homotopy invariants of braided commutative algebras and the Deligne conjecture for finite tensor categories ⋮ Strong 1-boundedness of unimodular orthogonal free quantum groups ⋮ Homotopy coherent mapping class group actions and excision for Hochschild complexes of modular categories ⋮ Topological generation and matrix models for quantum reflection groups

Cites Work

• Paths in quantum Cayley trees and \(L^{2}\)-cohomology
• The Baum-Connes conjecture for free orthogonal quantum groups
• Frobenius and separable functors for generalized module categories and nonlinear equations
• Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups
• Dualising complexes and twisted Hochschild (co)homology for Noetherian Hopf algebras.
• Duality and products in algebraic (co)homology theories.
• Homology of free quantum groups
• Hochschild and cyclic homology of quantum groups
• Cohomology of quantum groups at roots of unity
• Semiperfect coalgebras
• Hopf modules and Yetter-Drinfel'd modules
• Crossed modules and Doi-Hopf modules
• Hopf-Galois systems
• Cohomology theories of Hopf bimodules and cup-product.
• Injective Hopf bimodules, cohomologies of infinite dimensional Hopf algebras and graded-commutativity of the Yoneda product.
• Free products of compact quantum groups
• \(L^{2}\)-cohomology for von Neumann algebras
• The quantum group of a nondegenerate bilinear form.
• The boundary of universal discrete quantum groups, exactness, and factoriality
• Integration over compact quantum groups
• A remark on support of the principal function for class A operators
• Twisted homology of quantum \(\text{SL}(2)\)
• Hopf–Galois Systems and Kashiwara Algebras
• Bialgebra Cohomology of the Duals of a Class of Generalized Taft Algebras
• Bialgebra cohomology, deformations, and quantum groups.
• $L^2$-homology for compact quantum groups
• A relation between Hochschild homology and cohomology for Gorenstein rings
• The Representation Category of the Quantum Group of a Non-degenerate Bilinear Form
• Hopf bigalois extensions
• IDENTIFICATION OF THE POISSON AND MARTIN BOUNDARIES OF ORTHOGONAL DISCRETE QUANTUM GROUPS
• L²-homology for von Neumann algebras

This page was built for publication: Hochschild homology of Hopf algebras and free Yetter–Drinfeld resolutions of the counit