Related papers: Groupoid Actions on Fractafolds

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…

Fredholm Lie groupoids were introduced by Carvalho, Nistor and Qiao as a tool for the study of partial differential equations on open manifolds. This article extends the definition to the setting of locally compact groupoids and proves that…

We consider the category of C*-algebras equipped with actions of a locally compact quantum group. We show that this category admits a monoidal structure satisfying certain natural conditions if and only if the group is quasitriangular. The…

A simple observation, showing that every groupoid becomes an inverse semigroup after adding one element. In such inverse semigroups all idempotents are mutually orthogonal. This fact implies that every C*-algebra of a discrete groupoid is a…

We give an explicit groupoid presentation of certain stacks of vector bundles on formal neighborhoods of rational curves inside algebraic surfaces. The presentation involves a M\"obius type action of an automorphism group on a space of…

We present natural and general ways of building Lie groupoids, by using the classical procedures of blowups and of deformations to the normal cone. Our constructions are seen to recover many known ones involved in index theory. The…

Let $A$ be a simple, exact, separable, unital $C^*$-algebra and let $\alpha \colon G \rightarrow Aut(A)$ be an action of a finite group $G$ with the weak tracial Rokhlin property. We show that every trace on $A \rtimes_{\alpha} G$ is…

We classify the possible images of the action of the group of automorphisms of a smooth Fano threefold on its Picard group. We also study the first group cohomology of the Picard group for families of smooth Fano threefolds.

We characterise the groupoid $C^*$-algebras associated to the transformation groupoids of injective actions of discrete countable Ore semi-groups on compact topological spaces in terms of the reduced crossed product from the dual actions,…

We study diagonal bimodules of \'{e}tale groupoid $C^*$-algebras over their canonical diagonal subalgebras, and establish necessary and sufficient conditions for such a bimodule to be spectral-that is, determined by its spectrum. For a…

An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the…

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…

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…

Let $G$ be a minimal locally compact groupoid with compact metrizable unit space and let $E$ be a continuous $G$-Hilbert bundle. We show that a bounded continuous cocycle $c: G\ra r^*E$ is necessarily a continuous coboundary. This is a…

This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…

Let $X$ be an algebraic variety over $\mathbb{C}$ and $G$ be an algebraic group acting on $X$ whose action is closed. J. Poineau defined a compactification $X^\urcorner$ of $X(\mathbb{C})$ by using hybrid Berkovich spaces. We will focus on…

Let a split element of a connected semisimple Lie group act on one of its flag manifolds. We prove that each connected set of fixed points of this action is itself a flag manifold. With this we can obtain the generalized Bruhat…

We extend the theory of Fourier--Stieltjes algebras to the category of twisted actions by \'etale groupoids on arbitrary C*-bundles, generalizing theories constructed previously by B\'{e}dos and Conti for twisted group actions on unital…

We introduce a definition of the locally trivial $G$-C*-algebra, which is a noncommutative counterpart of the total space of a locally compact Hausdorff numerable principal $G$-bundle. To obtain this generalization, we have to go beyond the…

We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and $ C^{\ast} $-algebras associated to these groupoids. We provide a new…