Related papers: Multiplicative partial isometries, manageability, …

The standard representation of c*-algebra is used to describe fields in compactified space-time dimensions characterized by topologies of the type $ \Gamma_{D}^{d}=(\mathbb{S}^{1})^{d}\times \mathbb{M}^{D-d}$. The modular operator is…

Mimicking the von Neumann version of Kustermans and Vaes' locally compact quantum groups, Franck Lesieur had introduced a notion of measured quantum groupoid, in the setting of von Neumann algebras. In this article, we suppose that the…

It shown that an a locally injective surjection on a compact metric space admits a canonical locally homeomorphic extension such that the associated C*-algebras are isomorphic. This is then used in a study of the possible inverse…

Consider the compact quantum group $U_q(2)$, where $q$ is a non-zero complex deformation parameter such that $|q|\neq 1$. Let $C(U_q(2))$ denote the underlying $C^*$-algebra of the compact quantum group $U_q(2)$. We prove that if $q$ is a…

We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility…

We show that the assignment of the (left) completely bounded multiplier algebra $M_{cb}^l(L^1(\mathbb G))$ to a locally compact quantum group $\mathbb G$, and the assignment of the intrinsic group, form functors between appropriate…

In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the `noncommutative Shilov boundary', and more particularly via the left multiplier operator algebra…

We study operator spaces, operator algebras, and operator modules, from the point of view of the `noncommutative Shilov boundary'. In this attempt to utilize some `noncommutative Choquet theory', we find that Hilbert C$^*-$modules and their…

We show that the class of unital $\mathrm{C}^*$-algebras is an elementary class in the language of operator systems. As a result, we have that there is a definable predicate in the language of operator systems that defines the…

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…

Following Robert's [26], we study the structure of unitary groups and groups of approximately inner automorphisms of unital $C^*$-algebras, taking advantage of the former being Banach-Lie groups. For a given unital $C^*$-algebra $A$, we…

We compare actions on C*-algebras of two constructions of locally compact quantum groups, the bicrossed product and the double crossed product. We give a duality between them as a generalization of Baaj-Skandalis duality. In the case of…

We define and show the existence of the quantum symmetry group of a Hilbert module equipped with an orthogonal filtration. Our construction unifies the constructions of Banica-Skalski's quantum symmetry group of a C*-algebra equipped with…

We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of…

Let $K$ be a compact metric space and let $\gamma = (\gamma_1, \dots, \gamma_n)$ be a system of proper contractions on $K$. We study a C*-algebra $\mathcal{MC}_{\gamma_1, \dots, \gamma_n}$ generated by all multiplication operators by…

The multipullback quantization of complex projective spaces lacks the naive quantum CW-complex structure because the quantization of an embedding of the $n$-skeleton into the $(n+1)$-skeleton does not exist. To overcome this difficulty, we…

For a $C^*$-algebra $A$ of compact operators and a compact manifold $M,$ we prove that the Hodge theory holds for $A$-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective $A$-Hilbert…

We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative…

In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a…

We consider three lifting questions: Given a $C\sp{*}$-algebra $I$, if there is a unital $C\sp{*}$-algebra $A$ contains $I$ as an ideal, is every unitary from $A/I$ lifted to a unitary in $A$? is every unitary from $A/I$ lifted to an…