Related papers: An Imprimitivity Theorem for Partial Actions

We initiate a careful study of a generalized symmetric imprimitivity theory for commuting proper actions of locally compact groups H and K on a C*-algebra.

Imprimitivity theorems provide a fundamental tool for studying the representation theory and structure of crossed-product C*-algebras. In this work, we show that the Imprimitivity Theorem for induced algebras, Green's Imprimitivity Theorem…

In the framework of locally compact quantum groups, we provide an induction procedure for unitary corepresentations as well as coactions on C*-algebras. We prove imprimitivity theorems that unify the existing theorems for actions and…

We study free and compact group actions on unital C*-algebras. In particular, we provide a complete classification theory of these actions for compact Abelian groups and explain its relation to the classical classification theory of…

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…

We introduce the notion of self-similar actions of grouopids on other groupoids and Fell bundles. This leads to a new imprimitivity theorem arising from such dynamics, generalizing many earlier imprimitivity theorems involving group and…

We define the notion of a partial action on a generalized Boolean algebra and associate to every such system and commutative unital ring $R$ an $R$-algebra. We prove that every strongly $E^{\ast}$-unitary inverse semigroup has an associated…

We provide a framework for studying concrete C*-algebras associated with algebraic actions of semigroups: Given such an action, we construct an inverse semigroup, and we introduce conditions for algebraic actions that characterize…

We associate a $C^*$-algebra to a partial action of the integers acting on the base space of a vector bundle, using the framework of Cuntz--Pimsner algebras. We investigate the structure of the fixed point algebra under the canonical gauge…

We introduce the notion of continuous twisted partial actions of a locally compact group on a C*-algebra. With such, we construct an associated C*-algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any…

Given a finite alphabet $\Lambda$, and a not necessarily finite type subshift $X\subseteq \Lambda^\infty$, we introduce a partial action of the free group $F(\Lambda)$ on a certain compactification $\Omega_X$ of $X$, which we call the…

In a recent paper the authors introduced universal and exotic generalized fixed-point algebras for weakly proper group actions on C*-algebras. Here we extend the notion of weakly proper actions to actions on Hilbert modules. As a result we…

Using the strong relation between coactions of a discrete group G on C*-algebras and Fell bundles over G, we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the…

We define the notion of action of an L-infinity algebra $g$ on a graded manifold $M$, and show that such an action corresponds to a homological vector field on $g[1] \times M$ of a specific form. This generalizes the correspondence between…

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional algebra of L(E) contains those of B and C as…

In this paper, by analogy with the case of C*-algebras, we define the notion of induced representation of a locally C*-algebra, and then we prove a imprimitivity theorem for induced representations of locally C*-algebras.

In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we…

This is a book about Partial Actions and Fell Bundles with applications to C*-algebras generated by partial isometries. Here is the table of contents: 1-Introduction, 2-Partial actions, 3-Restriction and globalization, 4-Inverse semigroups,…