Related papers: C*-algebras associated with some second order diff…

We define and systematically study nonassociative C*-algebras as C*-algebras internal to a topological tensor category. We also offer a concrete approach to these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded operators…

We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of a preceding paper and providing a simple algebraic approach to the theory of pseudodifferential operators in settings…

It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states.…

Consider the Plancherel decomposition of the tensor product of a highest weight and a lowest weight unitary representations of $SL_2$. We construct explicitly the action of the Lie algebra $sl_2 + sl_2$ in the direct integral of Hilbert…

We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic…

In this paper, we present a captivating construction by Grothendieck, originally formulated for algebraic varieties, and adapt it to the realm of C*-algebras. Our main objective is to investigate the conditions under which this particular…

It has been a longstanding problem whether every amenable operator algebra is isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a nonseparable counterexample. The existence of a separable counterexample remains an open…

We study self-similar groupoid actions on arbitrary directed graphs together with $\mathbb{T}$-valued twists that exhaust the second cohomology group of the associated Zappa-Sz\'ep product category. We define and analyse the associated…

Algebras associated with Quantum Electrodynamics and other gauge theories share some mathematical features with T-duality Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be…

We compute the two-cocycles (or multipliers) of the free nilpotent groups of class $2$ and rank $n$ and give conditions for simplicity of the corresponding twisted group $C^*$-algebras. These groups are representation groups for…

We classify graph C*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph. This is done by a purely graph theoretical calculation of the K-theory and the position of the unit…

We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…

We give a structural characterisation of linear operators from one $C^\ast$% -algebra into another whose adjoints map extreme points of the dual ball onto extreme points. We show that up to a $\ast$-isomorphism, such a map admits of a…

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L^{\pm} functionals are constructed and the dual algebra is derived explicitly. These functionals are then…

The spectrum of a selfadjoint second order elliptic differential operator in $L^2(\mathbb{R}^n)$ is described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a multi-dimensional Glazman decomposition and…

We study the 2-adic version of the ring $C^*$-algebra of the integers. First, we work out the precise relation between the Cuntz algebra $\cO_2$ and our 2-adic ring $C^*$-algebra in terms of representations. Secondly, we prove a 2-adic…

Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality…

In this paper we suggest a definition for a C*-algebra attached to an injective morphism of some \'Etale groupoid. We take into account all the peculiarities of such objects and present some interesting relations with already well-known…

A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their…

Following our previous works on $C^*$-graph algebras and the associated Cuntz-Krieger graph families, in this paper we will try to have a look at the colored version of these structures and to see what a $C^*$-colored graph algebra might…