Related papers: Some Examples of Bicrossed Products with the Rapid…
We study the rapid decay property and polynomial growth for duals of bicrossed products coming from a matched pair of a discrete group and a compact group
We make a comprehensive and self-contained study of compact bicrossed products arising from matched pairs of discrete groups and compact groups. We exhibit an automatic regularity property of such a matched pair and and produce an easy…
For a matched pair of locally compact quantum groups, we construct the double crossed product as a locally compact quantum group. This construction generalizes Drinfeld's quantum double construction. We study C*-algebraic properties of…
The cocycle bicrossed product construction allows certain freedom in producing examples of locally compact quantum groups. We give an overview of some recent examples of this kind having remarkable properties.
We prove that the rapid decay property (RD) of groups is preserved by graph products defined on finite simplicial graphs.
Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are…
We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that…
We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group $\Gamma := \mathbf{SL}_2(A)$, where $A := \mathbb{F}_q[X,X^{-1}]$ is the ring of Laurent polynomials with…
This work concerns a generalization of property (RD) from discrete groups to twisted \'etale groupoids equipped with a length function. We show that, under the assumption that the \'etale groupoid is principal, twisted property (RD) is…
We investigate connections between various rigidity and softness properties for discrete quantum groups. After introducing a notion of residual finiteness, we show that it implies the Kirchberg factorization property for the discrete…
Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological…
This is a survey of methods of proving or disproving the Rapid Decay property in groups. We present a centroid property of group actions on metric spaces. That property is a generalized (and corrected) version of the property (**)-relative…
We characterize the hypocompact radical of a semicrossed product in terms of properties of the dynamical system. We show that an element A of a semicrossed product is in the hypocompact radical if and only if the Fourier coefficients of A…
We introduce a notion of the Rapid Decay Property (RDP) for Fell bundles over locally compact Hausdorff \'etale groupoids, extending earlier rapid decay theories for \'etale groupoids and twists. Our approach yields analytic control on…
The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law. The equivalence between quasicrossed products and…
We define and provide some basic analysis of various types of crossed products by semimultiplicative sets, and then prove a $KK$-theoretical descent homomorphisms for semimultiplicative sets in accord with the descent homomorphism for…
We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…
In the framework of locally compact quantum groups, we study cocycle actions. We develop the cocycle bicrossed product construction, starting from a matched pair of locally compact quantum groups. We define exact sequences and establish a…
The main aim of this paper is to introduce some examples of non-compact locally compact quantum groups to a non-specialized audience. The major importance of these examples is their simplicity. Other examples as the quantum E(2) group of…
We study how solid closure in mixed characteristic behaves after taking ultraproducts. The ultraproduct will be chosen so that we land in equal characteristic, and therefore can make a comparison with tight closure. As a corollary we get an…