Related papers: Noncommutative Lattices and Their Continuum Limits

Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by classical Lipschitz seminorms that produce compact quantum…

We survey noncommutative spacetimes with coordinates being enveloping algebras of Lie algebras. We also explain how to do differential geometry on noncommutative spaces that are obtained from commutative ones via a Moyal-product type…

The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…

We propose a general scheme for the "logic" of elementary propositions of physical systems, encompassing both classical and quantum cases, in the framework given by Non Commutative Geometry. It involves Baire*-algebras, the non-commutative…

We study a class of matrix function algebras, here denoted $\mathcal{T}^{+}(\mathcal{C}_n)$. We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of…

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 associate to each unital $C^*$-algebra $A$ a geometric object---a diagram of topological spaces representing quotient spaces of the noncommutative space underlying $A$---meant to serve the role of a generalized Gel'fand spectrum. After…

Let $X$ be a compact metric space which is locally absolutely retract and let $\phi: C(X)\to C(Y, M_n)$ be a unital homomorphism, where $Y$ is a compact metric space with ${\rm dim}Y\le 2.$ It is proved that there exists a sequence of $n$…

We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present certain corollaries of this result.

It is shown that the algebra of continuous functions on the quantum $2n+1$-dimensional lens space $C(L^{2n+1}_q(N; m_0,\ldots, m_n))$ is a graph $C^*$-algebra, for arbitrary positive weights $ m_0,\ldots, m_n$. The form of the corresponding…

Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using…

We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…

In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…

We study the noncommutative topology of the $C^*$-algebras $C(\mathbb{C}P_q^{n})$ of the quantum projective spaces within the framework of Kasparov's bivariant K-theory. In particular, we construct an explicit KK-equivalence with the…

In this paper we study the C*-envelope of the (non-self-adjoint) tensor algebra associated via subproduct systems to a finite irreducible stochastic matrix $P$. Firstly, we identify the boundary representations of the tensor algebra inside…

Let A be a unital separable simple infinite-dimensional nuclear C*-algebra with at least one tracial state. We prove that if the trace space of A has compact finite-dimensional extreme boundary then there exist unital embeddings of matrix…

We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under…

The aim of this paper is to investigate the links between ${\cal T}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\cal T}_C$-class sequences…

We solve the lifting problem in C^*-algebras for many sets of relations that include the relations x_j^{N_j} = 0 on each variable. The remaining relations must be of the form \| p(x_1,...,x_n) \| \leq C for C a positive constant and p a…

In this paper, we introduce a new technique in the study of the $*$-regular closure of some specific group algebras $KG$ inside $\mathcal{U}(G)$, the $*$-algebra of unbounded operators affiliated to the group von Neumann algebra…