Related papers: Supramenable groups and partial actions

We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint…

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…

Suppose that $\alpha$ is an action of the semigroup $\mathbb{N}^{2}$ on a $C^*$-algebra $A$ by endomorphisms. Let $A\times_{\alpha}^{\textrm{piso}} \mathbb{N}^{2}$ be the associated partial-isometric crossed product. By applying an earlier…

Let G be a group and let A be the algebra of complex functions on G with finite support. The product in G gives rise to a coproduct on A making it a multiplier Hopf algebra. In fact, because there exist integrals, we get an algebraic…

We provide an equivariant extension of the bivariant Cuntz semigroup introduced in previous work for the case of compact group actions over C*-algebras. Its functoriality properties are explored and some well-known classification results…

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…

von Neumann algebras have been playing an increasingly important role in the context of gauge theories and gravity. The crossed product presents a natural method for implementing constraints through the commutation theorem, rendering it a…

Given an inverse semigroup $S$ endowed with a partial action on a topological space $X$, we construct a groupoid of germs $S\ltimes X$ in a manner similar to Exel's groupoid of germs, and similarly a partial action of $S$ on an algebra $A$…

A subspace Y of a separable metrizable space X is separable, but without X metrizable this is not true even If Y is a closed linear subspace of a topological vector space X. K.H. Hofmann and S.A. Morris introduced the class of pro-Lie…

Let $G$ be a locally compact, Hausdorff, second countable groupoid and $A$ be a separable, $C_0(G^{(0)})$-nuclear, $G$-$C^*$-algebra. We prove the existence of quasi-invariant, completely positive and contractive lifts for equivariant,…

The notion of a multiplier of a group X is generalized to that of a C*-multiplier by allowing it to have values in an arbitrary C*-algebra A. On the other hand, the notion of the action of X in A is generalized to that of a projective…

We construct an example of a simple nuclear separable unital stably finite Z-stable C*-algebra along with an action of the circle such that the crossed product is simple but not Z-stable.

In this article, we establish maximal inequalities and deduce ergodic theorems for state-preserving actions of amenable, locally compact, second-countable groups on tracial non-commutative $L^1$-spaces. As a further consequence, in…

We consider an action of a compact group whose dual is archimedean linearly ordered or a direct product (or sum) of such groups on a von Neumann algebra, M. We define the generalized Hardy subspace of the Hilbert space of a standard…

Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe such symmetries using crossed modules of groupoids. We define actions of crossed modules on C*-algebras and crossed…

We take a new look at dilation theory for nonself-adjoint operator algebras. Among the extremal (co)extensions of a representation, there is a special property of being fully extremal. This allows a refinement of some of the classical…

We introduce the notion of a ``sofic $\mathcal{C}$-action'' of one group on another by automorphisms, for $\mathcal{C}$ a class of groups. We show that if $\mathcal{C}$ is the class of (i) sofic, (ii) hyperlinear, (iii) linear sofic or (iv)…

We study the ideal structure of reduced crossed product of topological dynamical systems of a countable discrete group. More concretely, for a compact Hausdorff space $X$ with an action of a countable discrete group $\Gamma$, we consider…

Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…

We consider group measure space II$_1$ factors $M=L^{\infty}(X)\rtimes\Gamma$ arising from Bernoulli actions of ICC property (T) groups $\Gamma$ (more generally, of groups $\Gamma$ containing an infinite normal subgroup with relative…