The \(K\)-theory of free quantum groups

DOI10.1007/s00208-013-0902-9zbMath1284.46063arXiv1112.3291OpenAlexW2088052735MaRDI QIDQ368625

Christian Voigt, Roland Vergnioux

Publication date: 23 September 2013

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3291

zbMATH Keywords

Baum-Connes conjecture\(K\)-groupsfree quantum group

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Quantum groups (quantized function algebras) and their representations (20G42) Kasparov theory ((KK)-theory) (19K35)

Related Items

Measured quantum groupoids on a finite basis and equivariant Kasparov theory ⋮ Quantum actions on discrete quantum spaces and a generalization of Clifford's theory of representations ⋮ \({L_{p}}\)-representations of discrete quantum groups ⋮ On the structure of quantum automorphism groups ⋮ On the Sobolev embedding properties for compact matrix quantum groups of Kac type ⋮ The Baum-Connes property for a quantum (semi-)direct product ⋮ Operator algebras of free wreath products ⋮ Introduction to compact (matrix) quantum groups and Banica-Speicher (easy) quantum groups ⋮ Hecke algebras and the Schlichting completion for discrete quantum groups ⋮ Thoma type results for discrete quantum groups ⋮ \(K\)-amenability of HNN extensions of amenable discrete quantum groups ⋮ Quantum reflections, random walks and cut-off ⋮ Graphs of quantum groups and \(K\)-amenability ⋮ Équivalence monoïdale de groupes quantiques et K-théorie bivariante ⋮ On the Baum–Connes conjecture for discrete quantum groups with torsion and the quantum Rosenberg conjecture ⋮ Quantum groups, from a functional analysis perspective ⋮ Permanence of approximation properties for discrete quantum groups ⋮ Noncommutative Borsuk-Ulam-type conjectures revisited ⋮ Induction for locally compact quantum groups revisited

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Baum-Connes conjecture for free orthogonal quantum groups
• The Baum-Connes conjecture via localisation of categories
• Equivariant Poincaré duality for quantum group actions
• Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups
• Homological algebra in bivariant \(K\)-theory and other triangulated categories. II
• Groups acting on buildings, operator \(K\)-theory, and Novikov's conjecture
• An algebraic framework for group duality
• The Baum-Connes conjecture and discrete group actions on trees
• The free compact quantum group \(U(n)\)
• Geometric \(K\)-theory for Lie groups and foliations
• Baum-Connes conjecture and group actions on trees
• \(C^*\)-algèbres de Hopf et théorie de Kasparov équivariante. (Hopf \(C^*\)-algebras and equivariant Kasparov theory)
• \(K\)-amenability for amalgamated free products of amenable discrete quantum groups
• Free products of compact quantum groups
• K-theoretic amenability for \(SL_ 2({\mathbb{Q}}_ p)\), and the action on the associated tree
• A new approach to induction and imprimitivity results
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• DOUBLE CROSSED PRODUCTS OF LOCALLY COMPACT QUANTUM GROUPS
• Orientation of quantum Cayley trees and applications
• K-theoretic amenability for discrete groups.
• LOCALLY COMPACT QUANTUM GROUPS IN THE UNIVERSAL SETTING
• UNIVERSAL QUANTUM GROUPS
• Locally compact quantum groups
• \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space

This page was built for publication: The \(K\)-theory of free quantum groups