Related papers: The boundary of universal discrete quantum groups,…

We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as…

We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…

Given an action of a discrete quantum group (in the sense of Van Daele, Kustermans and Effros-Ruan) ${\cal A}$ on a $C^*$-algebra ${\cal C}$, satisfying some regularity assumptions resembling the proper $\Gamma$-compact action for a…

We study quotients of the Toeplitz C*-algebra of a random walk, similar to those studied by the author and Markiewicz for finite stochastic matrices. We introduce a new Cuntz-type quotient C*-algebra for random walks that have convergent…

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…

This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…

We study the quantum isometry groups of the noncommutative Riemannian manifolds associated to discrete group duals. The basic representation theory problem is to compute the law of the main character of the relevant quantum group, and our…

We show that the discrete duals of the universal unitary quantum groups and orthogonal quantum groups have Kirchberg's factorization property when n is different from 3.

For a discrete group G, we consider the minimal C*-subalgebra of $\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant projection. This algebra always exists and is unique up to isomorphism. It is trivial if and only…

We show that the discrete duals of the free orthogonal quantum groups have the Haagerup property and the completely contractive approximation property. Analogous results hold for the free unitary quantum groups and the quantum automorphism…

This paper is concerned with random walks on a family of dyadic-valued solvable matrix groups. A description of the Poisson boundary of these groups for probability measures of finite first moment and non-zero displacements (or drifts) is…

We propose a definition of partition quantum spaces. They are given by universal $C^*$-algebras whose relations come from partitions of sets. We ask for the maximal compact matrix quantum group acting on them. We show how those fit into the…

In this paper, we introduce quotients of \'etale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an \'etale groupoid…

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

We study the quotients of the Toeplitz C*-algebra of a quasi-lattice ordered group (G,P), which we view as crossed products by a partial actions of G on closed invariant subsets of a totally disconnected compact Hausdorff space, the Nica…

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns…

In this paper we associate to every reduced C*-algebraic quantum group A a universal C*-algebraic quantum group. We fine tune a proof of Kirchberg to show that every *-representation of a modified L1-space is generated by a unitary…

Let $\Gamma$ be an $\widetilde A_2$ subgroup of $\PGL_3(\mathbb K)$, where $\mathbb K$ is a local field with residue field of order $q$. The module of coinvariants $C(\mathbb P^2_{\mathbb K},\mathbb Z)_{\Gamma}$ is shown to be finite, where…

The group of affine transformations with rational coefficients acts naturally on the real line, but also on the $p$-adic fields. The aim of this note is to show that, for random walks whose laws have a finite first moment, all these actions…