Related papers: Noncommutative Local Systems
We associate a non-commutative $C^*$-algebra with any locally finite simplicial complex. We determine the $K$-theory of these algebras and show that they can be used to obtain a conceptual explanation for the Baum-Connes conjecture.
In this paper we put forward the definition of particular subsets on a unital C*-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
We consider *-linear maps into a commutative C*-algebra C (X) of continuous functions on a locally compact Hausdorff space X with certain specified properties and prove two results: (1) an extension result for a class of *-linear maps Y -->…
Topological complexity for spaces was introduced by M. Farber as a minimal number of continuity domains for motion planning algorithms. It turns out that this notion can be extended to the case of not necessarily commutative C*-algebras.…
We consider a construction of C*-algebras from continuous piecewise monotone maps on the circle which generalizes the crossed product construction for homeomorphisms and more generally the construction of Renault, Deaconu and…
We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…
We propose a new generalization of neural network parameter spaces with noncommutative $C^*$-algebra, which possesses a rich noncommutative structure of products. We show that this noncommutative structure induces powerful effects in…
We introduce and study locally AW*-algebras (Baer locally C*-algebras) as a locally multiplicatively-convex generalization of AW*-algebras of Kaplansky. Among other basic properties of these algebras, it is established that: {\bullet} A…
After introducing a noncommutative counterpart of commutative algebraic geometry based on monoidal categories of quasi-coherent sheaves we show that various constructions in noncommutative geometry (e.g. Morita equivalences, Hopf-Galois…
We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…
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…
Noncommutative geometry is used to study the local geometry of ultrametric spaces and the geometry of trees at infinity. Connes's example of the noncommutative space of Penrose tilings is interpreted as a non-Hausdorff orbit space of a…
Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact (second countable) Hausdorff spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and in turn, a…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
In this note, making use of noncommutative $l$-adic cohomology, we extend the generalized Riemann hypothesis from the realm of algebraic geometry to the broad setting of geometric noncommutative schemes in the sense of Orlov. As a first…
The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of…
We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in…
It is known that any covering space of a topological group has the natural structure of a topological group. This article discusses a noncommutative generalization of this fact. A noncommutative generalization of the topological group is a…
We consider a locally compact Hausdorff groupoid $G$, and twist by a more general locally compact Hausdorff abelian group $\Gamma$ rather than the complex unit circle $\mathbb{T}$. We investigate the construction of $C^*$-algebras in…