Related papers: Co-Amenability of compact quantum groups
Let $M$ be a Hopf--von Neuman algebra with the predual $M_*$ and $WAP(M)$ the subspace in $M$ composed of weakly almost periodic functionals on $M_*$. The main example of such an algebra is $M=L^\infty(\mathbb G)$ for a locally compact…
This is Part II in our multi-part series of papers developing the theory of a subclass of locally compact quantum groupoids ("quantum groupoids of separable type"), based on the purely algebraic notion of weak multiplier Hopf algebras. The…
We give some sufficient conditions for the injectivity of actions of compact quantum groups on $C^{\ast}$-algebra. As an application, we prove that any faithful smooth action by a compact quantum group on a compact smooth (not necessarily…
We give a definition of amenability at infinity for a locally compact, $\sigma$-compact and Hausdorff etale groupoid and we study in some case the exactness of the reduced $C^*$-algebra of a such groupoid.
We classify the cosemisimple Hopf algebras whose corepresentation semi-ring is isomorphic to that of GL(2). This leads us to define a new family of Hopf algebras which generalize the quantum similitude group of a non-degenerate bilinear…
In this paper we show that the $\mathrm{K}$-homology groups of a separable C*-algebra can be enriched with additional descriptive set-theoretic information, and regarded as definable groups. Using a definable version of the Universal…
Quantum groups have been studied within several areas of mathematics and mathematical physics. This has led to different approaches, each of them with their own techniques and conventions. Starting with Hopf algebras, where there is a…
A regular way to define an additive coproduct (or ``coaddition'') on the q-deformed differential complexes is proposed for quantum groups and quantum spaces related to the Hecke-type R-matrices. Several examples of braided coadditive…
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions, and universal quantum groups,…
A family of algebra maps $H\to A_i$ whose common domain is a Hopf algebra is said to be jointly inner faithful if it does not factor simultaneously through a proper Hopf quotient of $H$. We show that tensor and free products of jointly…
We prove an analogue of the Baum-Connes conjecture for free orthogonal quantum groups. More precisely, we show that these quantum groups have a $ \gamma $-element and that $ \gamma = 1 $. It follows that free orthogonal quantum groups are $…
We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.
Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous correpresentations of $C^*$-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is…
We develop a theory of commensurability of groups, of rings, and of modules. It allows us, in certain cases, to compare sizes of automorphism groups of modules, even when those are infinite. This work is motivated by the Cohen-Lenstra…
We investigate the behavior of infinite-time admissibility under compact perturbations. We show, by means of two completely different examples, that infinite-time admissibility is not preserved under compact perturbations $Q$ of the…
We explore an application of homological algebra to set theoretic objects by developing a cohomology theory for Hausdorff gaps. The cohomology theory is introduced with enough generality to be applicable to other questions in set theory.…
We describe conditions that characterize amenability for groups in terms of positive definite functions valued in a von Neumann algebra.
We show that for topological groups and loop contractible coefficients the cohomology groups of continuous group cochains and of group cochains that are continuous on some identity neighbourhood are isomorphic. Moreover, we show a similar…
A generalized Hopf algebra structure for the positive (negative) part of the Drinfeld-Jimbo quantum group of type A_n is established without make any use of the usual deformation of the abelian part of sl_{n+1}.
We give a definition of an amenable fusion module over a fusion algebra. A notion of relative integrability for the `coduals' of coideals of compact quantum groups was recently introduced in the joint work of de Commer and Dzokou Talla. We…