Related papers: Crossed products whose unit group is locally solva…
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 define the notion of a principal S-bundle where S is a groupoid group bundle and show that there is a one-to-one correspondence between principal S-bundles and elements of a sheaf cohomology group associated to S. We also define the…
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 this paper, we study the residual solvability of the generalized free product of solvable groups.
We introduce the concept of crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system.…
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…
For a twisted partial action \Theta of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A X_\Theta G is proved to be associative. Given a G-graded k-algebra B =…
We study stability properties of amenable locally compact quantum groups under the bicrossed product construction. We obtain as our main result an equivalence between amenability of the bicrossed product and amenability of the matched…
The crossed products of locally C*-algebras are defined and a Takai duality theorem for inverse limit actions of a locally compact group on a locally C*-algebra is proved.
All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.
It is shown that quantum Euclidean groups $E_q(2)$, $E_\kappa(2)$ and $E_\kappa(3)$ have the structure of generalised crossed products.
We prove that if a totally disconnected locally compact group admits a topologically free boundary, then the reduced crossed product of continuous functions on its Furstenberg boundary by the group is simple. We also prove a partial…
It is shown that a closed solvable subgroup of a connected Lie group is compactly generated. In particular, every discrete solvable subgroup of a connected Lie group is finitely generated. Generalizations to locally compact groups 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…
A graded tensor category over a group $G$ will be called a crossed product tensor category if every homogeneous component has at least one multiplicatively invertible object. Our main result is a description of the crossed product tensor…
The category of crossed complexes gives an algebraic model of the category of $CW$-complexes and cellular maps. We explain basic results on crossed complexes which allow the computation of free crossed resolutions of graph products of…
We prove that the crossed product A x G of a separable, unital, quasidiagonal C*- algebra A by a discrete, countable, amenable, maximally almost periodic group G is quasidiagonal, provided that the action is almost periodic.
For any central simple algebra over a field F which contains a maximal subfield M with non-trivial F-automorphism group G, G is solvable if and only if the algebra contains a finite chain of subalgebras which are generalized cyclic algebras…
Let $G$ be a second countable, locally compact groupoid with Haar system, and let $\mathcal{A}$ be a bundle of $C^{\ast}$-algebras defined over the unit space of $G$ on which $G$ acts continuously. We determine conditions under which the…
In [J.M. Fern\'andez Vilaboa, R. Gonz\'alez Rodr\'iguez and A.B. Rodr\'iguez Raposo: Preunits and weak crossed products. J. of Pure Appl. Algebra 213, 2244-2261 (2009)] the notion of a weak crossed product of an algebra by an object, both…