Related papers: Full duality for coactions of discrete groups

In this paper we study free actions of groups on separated graphs and their \cstar{}algebras, generalizing previous results involving ordinary (directed) graphs. We prove a version of the Gross-Tucker Theorem for separated graphs yielding a…

We construct a weak conditional expectation from the section C*-algebra of a Fell bundle over a unital inverse semigroup to its unit fibre. We use this to define the reduced C*-algebra of the Fell bundle. We study when the reduced…

We prove that an outer action of a locally compact group $G$ on a full factor $M$ is automatically strictly outer, meaning that the relative commutant of $M$ in the crossed product is trivial. If moreover the image of $G$ in the outer…

Let $\Gamma$ be a discrete group. To every ideal in $\ell^{\infty}(\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general…

Let G be a group and let P be a subsemigroup of G. In order to describe the crossed product of a C*-algebra A by an action of P by unital endomorphisms we find that we must extend the action to the whole group G. This extension fits into a…

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…

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…

Let $A$ and $B$ be $C^*$-algebras with $A\subseteq M(B)$. Exploiting the duality between sober spaces and spatial locales, and the adjunction between restriction and induction for ideals in $A$ and $B$, we identify conditions that allow to…

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…

We consider two saturated Fell bundles over a countable discrete group, whose unit fibers are $\sigma$-unital $C^*$-algebras. Then by taking the reduced cross-sectional $C^*$-algebras, we get two inclusions of $C^*$-algebras. We suppose…

We study the C*-algebra crossed product $C_0(X)\rtimes G$ of a locally compact group $G$ acting properly on a locally compact Hausdorff space $X$. Under some mild extra conditions, which are automatic if $G$ is discrete or a Lie group, we…

Given a coaction $\delta$ of a locally compact group $G$ on a $\mathrm{C}^*$-algebra $A$, we study the relationship between two different forms of coaction invariance of ideals of $A$ and the ideals of the corresponding crossed product…

We will show a centrally free action of an amenable rigid C$^*$-tensor category on a properly infinite von Neumann algebra has the Rohlin property. This enables us to prove the fullness of the crossed product of a full factor by minimal…

We study actions of discrete groups on 2-categories. The motivating examples are actions on the 2-category of representations of finite tensor categories and their relation with the extension theory of tensor categories by groups.…

We prove that a discrete quantum group $\mathbb{G}$ has the approximation property if and only if a Fej\'{e}r-type representation holds for its $C^*$-algebraic or von Neumann algebraic crossed products. As applications, we extend several…

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…

Given an action $G \curvearrowright X$ of a discrete and countable infinite group $G$ on a compact and Hausdorff space $X$, we regard $\ell^1(G\curvearrowright X)$ as the Banach *-algebra crossed product associated to the action. We…

We define inverse semigroup actions on topological groupoids by partial equivalences. From such actions, we construct saturated Fell bundles over inverse semigroups and non-Hausdorff \'etale groupoids. We interpret these as actions on…

We prove the index theorem for elliptic operators acting on sections of bundles where fiber is equal to a projective module over a C*-algebra, in the situation of action of a compact Lie group on this algebra as well as on the total space…

The duality theorem for Coleff-Herrera products on a complex manifold says that if $f = (f_1,\dots,f_p)$ defines a complete intersection, then the annihilator of the Coleff-Herrera product $\mu^f$ equals (locally) the ideal generated by…