Co-Amenability of compact quantum groups

Abstract

We study the concept of co-amenability for a compact quantum group. Several conditions are derived that are shown to be equivalent to it. Some consequences of co-amenability that we obtain are faithfulness of the Haar integral and automatic norm-boundedness of positive linear functionals on the quantum group's Hopf *-algebra (neither of these properties necessarily holds without co-amenability).

25 pages. LaTex

References in corpus (3)

• Co-Amenability of compact quantum groups
• Fusion rules for representations of compact quantum groups
• Locally compact quantum groups in the universal setting

Cited by in corpus (47)

• Co-Amenability of compact quantum groups
• Symmetries of Lévy processes on compact quantum groups, their Markov semigroups and potential theory
• A Characterization of right coideals of quotient type and its application to classification of Poisson boundaries
• Quantum symmetry groups of C*-algebras equipped with orthogonal filtrations
• The Martin boundary of a discrete quantum group
• A New Characterisation of Idempotent States on Finite and Compact Quantum Groups
• Around Property (T) for quantum groups
• Remarks on the Quantum Bohr Compactification
• On quantum maps into quantum semigroups
• Multiplier Hopf algebras imbedded in C${}^{\ast }$-algebraic quantum groups
• Infinite-dimensional Compact Quantum Semigroup
• $L_p$-Representations of Discrete Quantum Groups
• Reflective-coreflective equivalence
• Quantum groups with projection and extensions of locally compact quantum groups
• Berezin quantization of noncommutative projective varieties
• Convergence of Fourier truncations for compact quantum groups and finitely generated groups
• Quantum automorphism groups of finite quantum groups are classical
• Higher l^2-Betti numbers of universal quantum groups
• Integration over the quantum diagonal subgroup and associated Fourier-like algebras
• Classification of actions of discrete Kac algebras on injective factors
• On C*-completions of discrete quantum group rings
• Applications of Foelner's condition to quantum groups
• Berezin Quantization From Ergodic Actions of Compact Quantum Groups, and Quantum Gromov-Hausdorff Distance
• A Kind of Compact Quantum Semigroups
• Mean ergodic theorem for amenable discrete quantum groups and a Wiener type theorem for compact metrizable groups
• Centrally free actions of amenable C${}^{\ast }$-tensor categories on von Neumann algebras
• Ergodic theory for quantum semigroups
• Invariant subsets under compact quantum group actions
• Haagerup approximation property via bimodules
• Deformations of spectral triples and their quantum isometry groups via monoidal equivalences
• Amenability and co-amenability of algebraic quantum groups II
• Amenability and co-amenability of algebraic quantum groups
• Amenable Discrete Quantum Groups
• On the zeroth L^2-homology of a quantum group
• Categorical aspects of compact quantum groups
• On Square Roots of the Haar State on Compact Quantum Groups
• On second cohomology of duals of compact groups
• Non existence of group structure on some quantum spaces
• Compact quantum metric spaces and ergodic actions of compact quantum groups
• An L^2-Kunneth formula for tracial algebras
• On amenability and co-amenability of algebraic quantum groups and their corepresentations
• Transitive Nonlocal Games
• Quantum symmetry groups of noncommutative tori
• Center of the algebra of functions on the quantum group $S{U}_q(2)$ and related topics
• On product type actions of G_q
• Compact quantum stabilizer subgroups
• A Note on Operator Biprojectivity of Compact Quantum Groups