Related papers: Crossed products by abelian semigroups via transfe…
We introduce a new notion of twisted actions of inverse semigroups and show that they correspond bijectively to certain regular Fell bundles over inverse semigroups, yielding in this way a structure classification of such bundles. These…
In this work, for a given inverse semigroup we will define the crossed product of an inverse semigroup by a partial action. Also, we will associate to an inverse semigroup $G$ an inverse semigroup $S_G$, and we will prove that there is a…
A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…
We introduce the notion of a bicocycle double cross product (resp. sum) Lie group (resp. Lie algebra), and a bicocycle double cross product bialgebra, generalizing the unified products. On the level of Lie groups the construction yields a…
We study the Toeplitz algebra $\TT(\N\rtimes\N^\times)$ and three quotients of this algebra: the $C^*$-algebra $\qn$ recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative boundary quotients. These…
We characterize the compact multiplication operators on a semi-crossed product in terms of the corresponding dynamical system. We also characterize the compact elements of this algebra and determine the ideal they generate.
The purpose of this paper is to introduce a consistent notion of universal and reduced crossed products by actions and coactions of groups on operator systems and operator spaces. In particular we shall put emphasis to reveal the full power…
We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical of these operator algebras. Furthermore, in the case the finite Blaschke product is…
We recall the abstract theory of Hopf algebra bicrossproducts and double cross products due to the author. We use it to develop some less-well known results about the quantum double as a twisting, as an extension and as $q$-Lorentz group.
One of pressing problems in mathematical physics is to find a generalized Poincar\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidirect product of groupoids $\Gamma_0 \rtimes…
We develop elliptic theory of operators associated with a diffeomorphism of a closed smooth manifold. The aim of the present paper is to obtain an index formula for such operators in terms of topological invariants of the manifold and of…
Let X be a Hilbert bimodule over a C*-algebra A and $O_X= A \rtimes_X \Z$. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on $s_{\xi} s_{\eta}^*$…
The notion of crossed product by a coquasi-bialgebra H is introduced and studied. The resulting crossed product is an algebra in the monoidal category of right H-comodules. We give an interpretation of the crossed product as an action of a…
This work explores the geometrical/algebraic framework of Lie algebroids, with a specific focus on the decoupling and coupling phenomena within the bicocycle double cross product realization. The bicocycle double cross product theory serves…
Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a…
We give an introduction into the ideal structure and representation theory of crossed products by actions of locally compact groups on C*-algebras. In particular, we discuss the Mackey-Rieffel-Green theory of induced representations of…
In this paper, we introduce the concept of crossed module for Hom-Leibniz-Rinehart algebras. We study the cohomology and extension theory of Hom-Leibniz-Rinehart algebras. It is proved that there is one-to-one correspondence between…
We introduce and study a homology theory of crossed modules with coefficients in an abelian crossed module. We discuss the basic properties of these new homology groups and give some applications. We then restrict our attention to the case…
We provide an equivariant extension of the bivariant Cuntz semigroup introduced in previous work for the case of compact group actions over C*-algebras. Its functoriality properties are explored and some well-known classification results…
Given two correspondences X and Y, we show that (under mild hypotheses) the Cuntz-Pimsner algebra of the tensor product of X and Y embeds as a certain subalgebra of the tensor product of the Cuntz-Pimsner algebra of X and the Cuntz=Pimsner…