Related papers: The ideal separation property for reduced group $C…
We study uniform perturbations of crossed product C$^*$-algebras by amenable groups. Given a unital inclusion of C$^*$-algebras $C\subseteq D$ and sufficiently close separable intermediate C$^*$-subalgebras $A$, $B$ for this inclusion with…
Given a closed ideal $I$ in a C*-algebra $A$, we develop techniques to bound the real rank of $A$ in terms of the real ranks of $I$ and $A/I$. Building on work of Brown, Lin and Zhang, we obtain complete solutions if $I$ belongs to any of…
A discrete group $\Gamma$ is called exact if the reduced group C*-algebra ${C_{\lambda}}^{*}(\Gamma)$ is exact as C*-algebras, and a discrete group $\Lambda$ is called residually exact if every nonunital element $g \in \Lambda$ admits a…
We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…
We introduce diagonal comparison, a regularity property of diagonal pairs where the sub-C*-algebra has totally disconnected spectrum, and establish its equivalence with the concurrence of strict comparison of the ambient C*-algebra and…
The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra…
We introduce the notion of a (noncommutative) C*-Segal algebra as a Banach algebra which is a dense ideal in a C*-algebra. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of…
We shall introduce the notion of the Picard group for an inclusion of $C^*$-algebras. We shall also study its basic properties and the relation between the Picard group for an inclusion of $C^*$-algebras and the ordinary Picard group.…
We study the elementary C*-algebra whose elements are the sum of a diagonal plus a compact operator. We describe the structure of the unitary group, the sets of ideals, automorhisms and projections.
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…
A simple Steinberg algebra associated to an ample Hausdorff groupoid $G$ is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space are infinite idempotents. If a simple Steinberg…
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 say that a C*-algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties of the spectrum, by divisibility properties in the Cuntz…
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived…
We characterise the strictly closed left invariant C*-subalgebras of the C*-algebra C_b(G) of bounded continuous functions on a locally compact group G. On the dual side, we characterise the strictly closed invariant C*-subalgebras of the…
Let $G$ be a locally compact groupoid. If $X$ is a free and proper $G$-space, then $(X*X)/G$ is a groupoid equivalent to $G$. We consider the situation where $X$ is proper but no longer free. The formalism of groupoid C*-algebras and their…
In this paper, we introduce the concept of ideal on CL-algebra. It is proved that this concept generalizes the notion of ideal on Residuated Lattices. Prime ideal on CL-algebra are defined and few interesting properties are obtained. It has…
We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a…
A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…
We obtain a description of the C*-algebras which can occur as a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension.