相关论文: The homotopy lifting theorem for semiprojective C*…
We investigate which relations for families of commuting matrices are stable under small perturbations, or in other words, which commutative $C^*$-algebras $C(X)$ are matricially semiprojective. Extending the works of Davidson,…
We show that every strongly $\mathbb{Z}$-graded C*-algebra (equivalently, every C*-algebra carrying a strongly continuous $\mathbb{T}$-action with full spectral subspaces) is a Cuntz--Pimsner algebra, and describe subalgebras and subspaces…
The aim of this paper is to develop the theory of Hom-coalgebras and related structures. After reviewing some key constructions and examples of quasi-deformations of Lie algebras involving twisted derivations and giving rise to the class of…
Within the framework of free actions of compact quantum groups on unital C*-algebras, we propose two conjectures. The first one states that, if $H$ is the C*-algebra of a compact quantum group coacting freely on a unital C*-algebra $A$,…
We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^*$-algebras that satisfy the UCT. More specifically, we show that the conjecture for the extension has an affirmative answer…
We continue the study of isomorphisms of tensor algebras associated to a C*-correspondences in the sense of Muhly and Solel. Inspired by by recent work of Davidson, Ramsey and Shalit, we solve isomorphism problems for tensor algebras…
Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver Q is a C*-correspondence, and from this correspondence one may…
We construct reduced and full semigroup C*-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due…
Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg algebras. This answers a folklore problem in rational…
Given a graph of C*-algebras, we prove a long exact sequence in KK-theory for both the maximal and the vertex-reduced fundamental C*-algebras in the presence of possibly non GNS-faithful conditional expectations. We deduce from it the…
The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…
We prove that faithful traces on separable and nuclear C*-algebras in the UCT class are quasidiagonal. This has a number of consequences. Firstly, by results of many hands, the classification of unital, separable, simple and nuclear…
We study non-counital coalgebras and their dual non-unital algebras, and introduce the finite dual of a non-unital algebra. We show that a theory that parallels in good part the duality in the unital case can be constructed. Using this, we…
We prove that a simple, separable, nuclear, purely infinite classifiable $C^*$-algebra is weakly semiprojective if and only if its $K$-groups are direct sums of cyclic groups.
In this paper, we prove that unital homomorphisms from continuous functions on a compact metric space to matrices over a C*-algebra with tracial rank at most one are approximately diagonalizable. We also consider some generalizations of…
In this paper, we introduce C*-algebraic partial compact quantum groups, which are quantizations of topological groupoids with discrete object set and compact morphism spaces. These C*-algebraic partial compact quantum groups are…
We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…
A C*-algebra is determined to a great extent by the partial order of its commutative C*-algebras. We study order-theoretic properties of this dcpo. Many properties coincide: the dcpo is, equivalently, algebraic, continuous, meet-continuous,…
We construct multi-brace cotensor Hopf algebras with bosonizations of quantum multi-brace algebras as examples. Quantum quasi-symmetric algebras are then obtained by taking particular initial data; this allows us to realize the whole…
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,…