Related papers: Proper actions of groupoids on $C^*$-algebras

If $G$ acts on a $C^*$-correspondence ${\mathcal H}$, then by the universal property $G$ acts on the Cuntz-Pimsner algebra ${\mathcal O}_{\mathcal H}$ and we study the crossed product ${\mathcal O}_{\mathcal H}\rtimes G$ and the fixed point…

We define the decomposition property for partial actions of discrete groups on $C^*$-algebras. Decomposable partial systems appear naturally in practice, and many commonly occurring partial actions can be decomposed into partial actions…

Let $n$ be a positive integer and $R=(M_{ij})_{1\leq i,j\leq n}$ be a generalized matrix ring. For each $1\leq i,j\leq n$, let $I_i$ be an ideal of the ring $R_i:=M_{ii}$ and denote $I_{ij}=I_iM_{ij}+M_{ij}I_j$. We give sufficient…

We study partial actions of exact discrete groups on C*-algebras. We show that the partial crossed product of a commutative C*-algebra by an exact discrete group is nuclear whenever the full and reduced partial crossed products coincide.…

We prove that the C*-algebra of the universal (n,m)-dynamical system may be obtained, up to Morita-Rieffel equivalence, as the crossed-product relative to an interaction on a commutative C*-algebra. The interaction involved is shown not to…

We consider $C^*$-algebras constructed from compact group actions on complex vector bundles $E\to X$ endowed with a Hermitian metric. An action of $G$ by isometries on $E\to X$ induces an action on the $C^*$-correspondence $\Gamma(E)$ over…

We study the exactness of the reduced crossed product of a semigroup dynamical system and the reduced $C^{*}$-algebra of a product system. We show that for a semigroup dynamical system $(A, P,\alpha)$, under reasonable hypotheses (e.g., $P$…

Using the group $G(1)$ of invertible elements and the maximal ideals $\mathfrak{m}_x$ of the commutative algebra $C(X)$ of real-valued functions on a compact regular space $X$, we define a Borel action of the algebra on the measure space…

We introduce the notion of a self-similar action of a groupoid $G$ on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodules, and thereby obtain corresponding universal…

A long-standing open question in the theory of group actions on C*-algebras is the stable rank of the crossed product. Specifically, N. C. Phillips asked that if a finite group $G$ acts on a simple unital C*-algebra $A$ with stable rank…

Recent results of Laca, Raeburn, Ramagge and Whittaker show that any self-similar action of a groupoid on a graph determines a 1-parameter family of self-mappings of the trace space of the groupoid C*-algebra. We investigate the fixed…

In the setting of product systems over group-embeddable monoids, we consider nuclearity of the associated Toeplitz C*-algebra in relation to nuclearity of the coefficient algebra. Our work goes beyond the known cases of single…

Let a discrete group $G$ act on a unital simple C$^*$-algebra $A$ by outer automorphisms. We establish a Galois correspondence $H\mapsto A\rtimes_{\alpha,r}H$ between subgroups of $G$ and C$^*$-algebras $B$ satisfying $A\subseteq B…

We investigate some consequences of a recent stabilization result of Ionescu, Kumjian, Sims, and Williams, which says that every Fell bundle $C^*$-algebra is Morita equivalent to a canonical groupoid crossed product. First we use the…

We present a new construction of crossed-product duality for maximal coactions that uses Fischer's work on maximalizations. Given a group $G$ and a coaction $(A,\delta)$ we define a generalized fixed-point algebra as a certain subalgebra of…

Consider the pair $(G,P)$ consisting of an abelian lattice-ordered discrete group $G$ and its positive cone $P$. Let $\alpha$ be an action of $P$ by extendible endomorphisms of a $C^*$-algebra $A$. We show that the Nica-Toeplitz algebra…

An action of a group $G$ on a set $X$ is called ``decent'' if every subgroup of $G$ with a finite orbit in $X$ fixes a point in $X$ and every finitely generated subgroup of $G$ such that every element of the subgroup fixes a point of $X$…

We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian…

For an action of a finite group on a C*-algebra, we present some conditions under which properties of the C*-algebra pass to the crossed product or the fixed point algebra. We mostly consider the ideal property, the projection property,…

Let $G$ be a locally compact abelian group. By modifying a theorem of Pedersen, it follows that actions of $G$ on $C^*$-algebras $A$ and $B$ are outer conjugate if and only if there is an isomorphism of the crossed products that is…