Related papers: Interactions
We interpret several constructions with C*-algebras as colimits in the bicategory of correspondences. This includes crossed products for actions of groups and crossed modules, Cuntz-Pimsner algebras of proper product systems, direct sums…
We introduce a method to define $C^*$-algebras from $C^*$-correspondences. Our construction generalizes Cuntz-Pimsner algebras, crossed products by Hilbert $C^*$-modules, and graph algebras.
We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is…
Certain $*$-semigroups are associated with the universal $C^*$-algebra generated by a partial isometry, which is itself the universal $C^*$-algebra of a $*$-semigroup. A fundamental role for a $*$-structure on a semigroup is emphasized, and…
We investigate how a correspondence coaction gives rise to a coaction on the associated Cuntz-Pimsner algebra. We apply this to recover a recent result of Hao and Ng concerning Cuntz-Pimsner algebras of crossed products of correspondences…
Quantum relations in the sense of Weaver are $M'$-bimodules, for a von Neumann algebra $M$, these generalising actual relations on a set $X$ when $M=\ell^\infty(X)$. Similarly, relations between two sets can be generalised as bimodules over…
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…
We introduce a method to study C*-algebras possessing an action of the circle group, from the point of view of its internal structure and its K-theory. Under relatively mild conditions our structure Theorem shows that any C*-algebra, where…
We interpret the construction of relative Cuntz-Pimsner algebras of correspondences in terms of the correspondence bicategory, as a reflector into a certain sub-bicategory. This generalises a previous characterisation of absolute…
Let G be a group and let P be a subsemigroup of G. In order to describe the crossed product of a C*-algebra A by an action of P by unital endomorphisms we find that we must extend the action to the whole group G. This extension fits into a…
Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…
The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev's crossed…
Partial dynamical systems (X,alpha) arise naturally when dealing with commutative C*-dynamical system (A,delta). We associate with every pair (X,alpha), or (A,delta), a covariance C*-algebra C*(X,alpha)=C*(A,delta) which agrees with a…
We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our…
Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our construction…
The article discusses the interrelation between relative Cuntz-Pimsner algebras and partial isometric crossed products, and presents a procedure that reduces any given Hilbert bimodule to the "smallest" Hilbert bimodule yielding the same…
By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal…
This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of…
When a locally compact group acts on a C*-correspondence, it also acts on the associated Cuntz-Pimsner algebra in a natural way. Hao and Ng have shown that when the group is amenable the Cuntz-Pimsner algebra of the crossed product…
We describe proper correspondences from graph C*-algebras to arbitrary C*-algebras by K-theoretic data. If the target C*-algebra is a graph C*-algebra as well, we may lift an isomorphism on a certain invariant to correspondences back and…