Related papers: Quantum spheres as graph C*-algebras: a review

The paper presents a detailed description of the K-theory and K-homology of C*-algebras generated by q-normal operators including generators and the index pairing. The C*-algebras generated by q-normal operators can be viewed as a…

We give a short proof of a recent theorem of Ionescu which shows that the Cuntz-Pimsner C*-algebra of a certain correspondence associated to a Mauldin-Williams graph is isomorphic to the graph algebra.

We describe a class of $C^*$-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space $C^*$-algebras of Matsumoto. In doing so we shed some new light on the different $C^*$-algebras that may be…

We prove that the isomorphism relation for separable C$^*$-algebras, and also the relations of complete and $n$-isometry for operator spaces and systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a…

We show how the Gelfand spectrum of certain commutative operator algebras can be studied based on the theorem of Stone and von Neumann. The method presented is a natural addition to the tools of quantum spectral synthesis, which were…

We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as…

Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…

We define C*-algebras on a Fock space such that the Hamiltonians of quantum field models with positive mass are affiliated to them. We describe the quotient of such algebras with respect to the ideal of compact operators and deduce…

Suppose we are given two graphs on $n$ vertices. We define an observable in the Hilbert space $\Co[(S_n \wr S_2)^m]$ which returns the answer ``yes'' with certainty if the graphs are isomorphic and ``no'' with probability at least…

The quantum even-dimensional balls are defined as the $C^*$-algebras generated by certain graphs. We exhibit a polynomial algebra for each even-dimensional quantum ball, and classify the irreducible representations of it.

Quantum graphs are defined by having a Laplacian defined on the edges of a metric graph with boundary conditions on each vertex such that the resulting operator, $\mathbf{L}$, is self-adjoint. We use Neumann boundary conditions although we…

In the present paper we study the structure of C*-$algebras generated by a certain *-algebra A and a partial isometry inducing an endomorphism of A.

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with…

In this paper, we characterize the C*-Algebra generated by partial isometries.

The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any…

Let $p(z,w)$ be a polynomial in two variables. We call the solution of the algebraic equation $p(z,w) = 0$ the algebraic correspondence. We regard it as the graph of the multivalued function $z \mapsto w$ defined implicitly by $p(z,w) = 0$.…

Let $\Sigma$ be a finite type surface, and $G$ a complex algebraic simple Lie group with Lie algebra $\mathfrak{g}$. The quantum moduli algebra of $(\Sigma,G)$ is a quantization of the ring of functions of $X_G(\Sigma)$, the variety of…

Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The fixed point algebras, termed quantum weighted Heegaard spheres, and their representations are classified and described on algebraic and topological levels. On the…

This thesis consists of two parts, both situated in operator theory, and both motivated by the quest for rigorous quantizations of gauge theories. The first part is based on [Skripka,vN - JST 2022], [van Suijlekom,vN - JNCG 2021], and [van…

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.…