Results 161 to 170 of about 525 (181)
Noncommutative space from dynamical noncommutative geometries
Journal of Geometry and Physics, 2009 : We present noncommutative topology as a basis for noncommutative geometry phrased completely in terms of partially ordered sets with operations. In this note we introduce a noncommutative space-time starting from a dynamical system of noncommutative ...
Freddy Van Oystaeyen
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Noncommutative Topologies, Localization, and Sheaves
Communications in Algebra, 2008In this note, we introduce and study the notion of sheaf on a noncommutative topology and construct an associated sheafification functor in this noncommutative context. It appears that abstract localization in the category of presheaves on a partially ordered set provides an elegant way to define this sheafification functor, generalizing similar ...
Aguilar, Judit Mendoza +2 more
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Noncommutative topological dynamics
Chaos, Solitons & Fractals, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Correia Ramos, C. +3 more
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Noncommutative topological dynamics
Proceedings of the London Mathematical Society, 2016When a group acts on a \(C^*\)-algebra \(A\), this induces actions on the Cuntz semigroup \(W(A)\) of \(A\) and on the \(K\)-theory group \(K_0(A)\). The present article studies to what extent important properties of the dynamics may be captured by these induced actions, which are much simpler than the original action.
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Noncommutative Topology: Spaces
2001The geometrical study of quadratic curves or surfaces, i.e., zero sets of second-degree polynomials, proceeds by examining points of intersection or tangent lines directly; but already for cubic curves it pays to examine first the ideal of all polynomials that vanish on the curve: in this way the study of an algebraic variety (the zero set of a given ...
José M. Gracia-Bondía +2 more
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NONCOMMUTATIVE GEOMETRY, QUANTIZATION AND TOPOLOGICAL ASPECTS OF A FERMION
International Journal of Modern Physics A, 2000It is pointed out here that noncommutative geometry having the space–time manifold X=M4×Z2 leads to the quantization of a fermion when the discrete space–time is incorporated as an internal variable. The chiral description of fermions in this geometry necessitates the introduction of a disconnected gauge group for the external Abelian field ...
Ghosh, P., Bandyopadhyay, P.
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Noncommutative Topology: Vector Bundles
2001We continue with our study of the duality between spaces and algebras by considering modules over these algebras. As we shall shortly see, C*- algebras have a supply of C*-modules on which they naturally act. In view of the Gelfand-Naimark theorem, one should ask whether a compact space M has topological partners corresponding to modules over C(M ...
José M. Gracia-Bondía +2 more
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Sketches of Noncommutative Topology
2022This thesis thematically divided into two parts. In the first part we are mastering C*-isomorphism problem by using various techniques applied to different examples of noncommutative algebraic varieties. In the second part we apply noncommutative homotopy theory to C*-algebraic objects related to manifold theory, in such a way deriving results and ...
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On the Topological Stable Rank of a Noncommutative Version of the Disc Algebra
Complex Analysis and Operator Theory, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ji, You Qing, Liu, Zhi, Zhang, Yuan Hang
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Index Theorems and Noncommutative Topology
2008These lecture notes are mainly devoted to a K-theory proof of the Atiyah-Singer index theorem. Some applications of the K-theory to noncommutative topology are also given.
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