相关论文: Quasi-Discrete Locally Compact Quantum Groups

We give a necessary and sufficient condition on a compact semitopological quantum semigroup which turns it into a compact quantum group. In particular, we obtain a generalisation of Ellis's joint continuity theorem. We also investigate the…

We give a rigorous account and prove continuity properties for the correspondence between almost flat bundles on a triangularizable compact connected space and the quasi-representations of its fundamental group. For a discrete countable…

The main result of the paper is the characterization of those locally compact quantum groups with projection, i.e. non-commutative analogs of semidirect products, which are extensions as defined by L. Vainerman and S. Vaes. It turns out…

We define and develop the notion of a discretisable quasi-action. It is shown that a cobounded quasi-action on a proper non-elementary hyperbolic space $X$ not fixing a point of $\partial X$ is quasi-conjugate to an isometric action on…

The Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and positive-definite functions established.…

A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie…

Let $\mathbb{H}\trianglelefteq\mathbb{G}$ be a closed normal subgroup of a locally compact quantum group. We introduce a strictly positive group-like element affiliated with $L^{\infty}(\mathbb{G})$ that, roughly, measures the failure of…

We characterize Lipschitz morphisms between quantum compact metric spaces as those *-morphisms which preserve the domain of certain noncommutative analogues of Lipschitz seminorms, namely lower semi-continuous Lip-norms. As a corollary,…

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in…

Any multiplier Hopf *-algebra} with positive integrals gives rise to a locally compact quantum group (in the sense of Kustermans and Vaes). As a special case of such a situation, we have the compact quantum groups (in the sense of…

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…

For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an…

For a net of C*-algebras on a discrete metric space, we introduce a bimodule version of the DHR tensor category and show it is an invariant of quasi-local algebras under isomorphisms with bounded spread. For abstract spin systems on a…

We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian…

Let $\mathcal{G}$ be a locally compact \'{e}tale groupoid and $\mathscr{L}(L^2(\mathcal{G}))$ be the $C^*$-algebra of adjointable operators on the Hilbert $C^*$-module $L^2(\mathcal{G})$. In this paper, we discover a notion called…

Let $A$ be a finite-dimensional Hopf algebra. The left and the right integrals on $A$ are related by means of a distinguished group-like element $\delta$ of $A$. Similarly, there is this element $\hat\delta$ in the dual Hopf algebra $\hat…

Let $G$ be a semi-simple real Lie group of real rank one and $\Gamma$ be a discrete subgroup in $G$ such that $\Gamma \backslash G$ has finite volume. We introduce a new group $C^*$-algebra $C^*_r(G, \Gamma)$, which provides a natural…

We propose a definition of compact quantum groupoids in the setting of C*-algebras, associate to such a quantum groupoid a regular C*-pseudo-multiplicative unitary, and use this unitary to construct a dual Hopf C*-bimodule and to pass to a…

Let \(G\) be a non-discrete, locally compact group with Haar measure \(m\). We prove that there exists a compact set \(K \subset G\) with \(m(K)=0\) such that \(KK^{-1}\) contains a neighborhood of the identity. Moreover, such a set may be…

In this short note we introduce a notion called "quantum injectivity" of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. Particularly, this provides a new characterization of amenability of…