Related papers: Properness conditions for actions and coactions

We investigate the ideal structures of the C^*-algebras arising from topological graphs. We give the complete description of ideals of such C^*-algebras which are invariant under the so-called gauge action, and give the condition on…

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…

It is known that exactness for a discrete group is equivalent to C*-exactness, i.e., the exactness of its reduced C*-algebra. The problem of whether this equivalence holds for general locally compact groups has recently been reduced by Cave…

The purpose of this paper is to provide tools for analyzing the compactness of sequences in Sobolev spaces, in particular if the sequence gets mapped onto a compact set by some nonlinear operator. Here, our focus lies on a very general…

We define equivariant semiprojectivity for C*-algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: arbitrary finite dimensional C*-algebras with arbitrary actions of…

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 show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is exact. This is a partial answer to a…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

A locally compact group $G$ has property PL if every isometric $G$-action either has bounded orbits or is (metrically) proper. For $p>1$, say that $G$ has property $BP_{L^p}$ if the same alternative holds for the smaller class of affine…

In this paper, we define the notions of full pro-$C^{*}$-crossed product, respectively reduced pro-$C^{*}$-crossed product, of a pro-$C^{*}$-algebra $A[\tau_{\Gamma}] $ by a strong bounded action $\alpha$ of a locally compact group $G$ 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…

We study smooth locally free actions of ${\mathbb R}^n$ on manifolds $M$ of dimension $n+1$. We are interested in compact orbits and in compact actions: actions with all orbits compact. Given a compact orbit in a neighborhood of compact…

For a number of properties of C*-algebras, including real rank zero, stable rank one, pure infiniteness, residual hereditary infiniteness, the combination of pure infiniteness and the ideal property, the property of being an AT algebra with…

Given a compact space X and two commuting continuous open surjective maps sigma_1, sigma_2 : X --> X, we construct certain C*-algebras that reflect the dynamics of the N^2-action. When the maps sigma_1, sigma_2 are local homeomorphisms,…

By combining R{\o}rdam's construction and the author's previous construction, we provide the first examples of amenable actions of non-amenable groups on simple separable nuclear C*-algebras that are neither stably finite nor purely…

Proper group actions are ubiquitous in mathematics and have many of the attractive features of actions of compact groups. In this survey, we discuss proper actions of Lie groups on smooth manifolds. If the group dimension is sufficiently…

We give the beginnings of the development of a theory of what we call "R-coactions" of a locally compact group on a $C^*$-algebra. These are the coactions taking values in the maximal tensor product, as originally proposed by Raeburn. We…

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…

In this paper, we investigate *-homomorphisms between C*-algebras associated to \'etale groupoids. First, we prove that such a *-homomorphism can be described by closed invariant subsets, groupoid homomorphisms and cocycles under some…

Actions of locally compact groups and quantum groups on W*-ternary rings of operators are discussed and related crossed products introduced. The results generalise those for von Neumann algebraic actions with proofs based mostly on passing…