Related papers: Equilibrium on Toeplitz extensions of higher dimen…

In this article, we prove $K$-stability for a family of $C^*$-algebras, which are generated by a finite set of unitaries and isometries satisfying twisted commutation relations. This family includes the $C^*$-algebra of doubly non-commuting…

Let $D$ be the irreducible bounded symmetric domain of $2\times2$ complex matrices that satisfy $ZZ^* < I_2$. The biholomorphism group of $D$ is realized by $\mathrm{U}(2,2)$ with isotropy at the origin given by…

Let $\zeta$ and $\eta$ be distinct points on the unit circle and suppose that $\phi$ is a linear-fractional self-map of the unit disk D, not an automorphism, with $\phi(\zeta)=\eta$. We describe the C*-algebra generated by the associated…

We present a $C^*$-algebra which is naturally associated to the $ax+b$-semigroup over $\mathbb N$. It is simple and purely infinite and can be obtained from the algebra considered by Bost and Connes by adding one unitary generator which…

We derive a well-behaved nonlinear extension of the non-relativistic Liouville-von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure state limit reduces to the usual Schroedinger…

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…

We verify the conjecture on continuous-trace subquotients for $C^*$-algebras of nilpotent linear dynamical systems, where by linear dynamical system we mean a continuous action of the additive group of real numbers by linear maps on a…

Generalizing the case of the Toeplitz algebra by Brake and Winter, we prove that the nuclear dimension of a C*-algebra extension of C(X) by the compact operators is equal to the dimension of X.

The universal C*-algebras of discrete product systems generalize the Toeplitz- Cuntz algebras and the Toeplitz algebras of discrete semigroups. We consider a semigroup P which is quasi-lattice ordered in the sense of Nica, and, for a…

This work investigates a quantum system described by a Hamiltonian operator in a two dimensional noncommutative space. The system consists of an electron subjected to a perpendicular magnetic field $\mathbf{B}$, coupled to a harmonic…

We associate to each discrete partial dynamical system a universal C*-algebra generated by partial isometries satisfying relations given by a Boolean algebra connected to the discrete partial dynamical system in question. We show that for…

Using ideas from Jones, lattice gauge theory and loop quantum gravity, we construct 1+1-dimensional gauge theories on a spacetime cylinder. Given a separable compact group $G$, we construct localized time-zero fields on the spatial torus as…

We prove that the quasi-homogenous symbols on the projective space $\mathbb{P}^n(\mathbb{C})$ yield commutative algebras of Toeplitz operators on all weighted Bergman spaces, thus extending to this compact case known results for the unit…

We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted C*-algebras. We also present an example of an inclusion of finitely aligned left-cancellative monoids that…

Given a dynamical system $(A,\al)$ where $A$ is a unital $\ca$-algebra and $\al$ is a (possibly non-unital) *-endomorphism of $A$, we examine families $(\pi,\{T_i\})$ such that $\pi$ is a representation of $A$, $\{T_i\}$ is a Toeplitz-Cuntz…

In this short note, we construct a variant of the Bohr topos of a C*-algebra which takes into account the topology of the algebra in a finer way and such that this construction is stable under pullback along geometric morphisms. This…

We show that the rotation algebras are limit of matrix algebras in a very strong sense of convergence for algebras with additional Lipschitz structure. Our results generalize to higher dimensional noncommutative tori and operator valued…

We define a notion of dynamical pressure at a self-adjoint element for a contractive completely positive self-map of an exact C*-algebra which adopts Voiculescu's approximation approach to noncommutative entropy and extends the…

Let A be a C*-algebra, h a Hilbert space and C the CAR algebra over h. We construct a twisted tensor product of A by C such that the two factors are not necessarily one in the relative commutant of the other. The resulting C*-algebra may be…

In recent work, Cuntz, Deninger and Laca have studied the Toeplitz type C*-algebra associated to the affine monoid of algebraic integers in a number field, under a time evolution determined by the absolute norm. The KMS equilibrium states…