Related papers: Maximal Coactions

Full C*-crossed products by actions of locally compact groups are characterized via the existence of suitable maximal coactions, in analogy with Landstad's characterization of reduced crossed products.

The graph C*-algebra of a directed graph E is the universal C*-algebra generated by a family of partial isometries satisfying relations which reflect the path structure of E. In the first part of this paper we consider coverings of directed…

Given a weak Kac system with duality $(\mathcal{H},V,U)$ arising from regular $\mathrm{C}^{*}$-algebraic locally compact quantum group $(\mathcal{G},\Delta)$, a $\mathrm{C}^{*}$-algebra $A$, and a sufficiently well-behaved coaction…

Given a coaction $\delta$ of a locally compact group $G$ on a $\mathrm{C}^*$-algebra $A$, we study the relationship between two different forms of coaction invariance of ideals of $A$ and the ideals of the corresponding crossed product…

An action on a G-space induces uniformities on the phase space. It is shown when the maximal G-compactification of a G-space can be obtained as a completion of the phase space with respect to one of these uniformities. Structure of G-spaces…

When S is a discrete subsemigroup of a discrete group G such that G = S^{-1} S, it is possible to extend circle-valued multipliers from S to G; to dilate (projective) isometric representations of S to (projective) unitary representations of…

Given a labeling c of the edges of a directed graph E by elements of a discrete group G, one can form a skew-product graph E cross_c G. We show, using the universal properties of the various constructions involved, that there is a coaction…

Let $G$ be a locally compact group. Then for every $G$-space $X$ the maximal $G$-proximity $\beta_G$ can be characterized by the maximal topological proximity $\beta$ as follows: $$ A \ \overline{\beta_G} \ B \Leftrightarrow \exists V \in…

We show that when a co-involutive Hopf C*-algebra $S$ coacts via $\delta$ on a C*-algebra $A$, there exists a full crossed product $A\times_\delta S$, with universal properties analogous to those of full crossed products by locally compact…

For any maximal coaction (A, G, delta) and any closed normal subgroup N of G, there exists an imprimitivity bimodule Y between the full crossed product A x G x N and A x G/N, together with a compatible coaction delta_Y of G. The assignment…

If B is C*-algebra of finite dimension n>3 then the finite dimensional irreducible representations of the compact quantum automorphism group of B, say G, have the same fusion rules as the ones of SO(3). As consequences, we get (1) a…

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 define the action of a locally compact group $G$ on a topological graph $E$. This action induces a natural action of $G$ on the $C^*$-correspondence ${\mathcal H}(E)$ and on the graph $C^*$-algebra $C^*(E)$. If the action is free and…

Using the close relationship between coactions of discrete groups and Fell bundles, we introduce a procedure for inducing a C*-coaction of a quotient group G/N of a discrete group G to a C*-coaction of G itself on an induced C*-algebra. We…

We extend the theory of tensor products of C*-algebras to the larger category of Fell bundles over locally compact groups. We prove that, like in the case of C*-algebras, there exist maximal and minimal tensor products. Given two Fell…

We consider the following problem. Suppose $\alpha$ is an action of a locally compact group $G$ on a $C^*$-algebra $A$, $H$ is a closed subgroup of $G$, and $(\pi,U)$ is a covariant representation of $(A,H,\alpha)$. For which closed…

Given a Lie group $G$ with finitely many components and a compact Lie group A which acts on $G$ by automorphisms, we prove that there always exists an A-invariant maximal compact subgroup K of G, and that for every such K, the natural map…

A coproduct on a vector space $A$ is defined as a linear map $\Delta:A\to A\otimes A$ satisfying coassociativity $(\Delta\otimes\iota)\Delta=(\iota\otimes\Delta)\Delta$. We use $\iota$ for the identity map. If $G$ is a finite group and if…

Given a partial action of a discrete group $G$ on a Hausdorff, locally compact, totally disconnected topological space $X$, we consider the correponding partial action of $G$ on the algebra $L_c(X)$ consisting of all locally constant,…

Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid.…