Gromov Hausdorff Distance For Quantum Metric Spaces Matrix Algebras Converge To The Sphere For Quantum Gromov Hausdorff Distance
DOWNLOAD
Download Gromov Hausdorff Distance For Quantum Metric Spaces Matrix Algebras Converge To The Sphere For Quantum Gromov Hausdorff Distance PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Gromov Hausdorff Distance For Quantum Metric Spaces Matrix Algebras Converge To The Sphere For Quantum Gromov Hausdorff Distance book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Gromov Hausdorff Distance For Quantum Metric Spaces Matrix Algebras Converge To The Sphere For Quantum Gromov Hausdorff Distance
DOWNLOAD
Author : Marc Aristide Rieffel
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Gromov Hausdorff Distance For Quantum Metric Spaces Matrix Algebras Converge To The Sphere For Quantum Gromov Hausdorff Distance written by Marc Aristide Rieffel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
By a quantum metric space we mean a $C DEGREES*$-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff di
Gromov Hausdorff Distance For Quantum Metric Spaces
DOWNLOAD
Author : Marc Aristide Rieffel
language : en
Publisher:
Release Date : 2014-09-11
Gromov Hausdorff Distance For Quantum Metric Spaces written by Marc Aristide Rieffel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Global differential geometry categories.
Gromov-Hausdorff distance for quantum metric spaces Bibliography Matrix algebras Converge to the sphere for quantum Gromov-Hausdorff distance Bibliography.
Points On Quantum Projectivizations
DOWNLOAD
Author : Adam Nyman
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Points On Quantum Projectivizations written by Adam Nyman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizataions, a significant class of examples in non-commutative algebraic geometry. More precisely, if $S$ is an affine, noetherian scheme, $X$ is a separated, noetherian $S$-scheme, $\mathcal{E}$ is a coherent ${\mathcal{O}}_{X}$-bimodule and $\mathcal{I} \subset T(\mathcal{E})$ is a graded ideal then we develop a compatibility theory on adjoint squares in order to construct the functor $\Gamma_{n}$ of flat families of truncated $T(\mathcal{E})/\mathcal{I}$-point modules of length $n+1$. For $n \geq 1$ we represent $\Gamma_{n}$ as a closed subscheme of ${\mathbb{P}}_{X^{2}}({\mathcal{E}}^{\otimes n})$.The representing scheme is defined in terms of both ${\mathcal{I}}_{n}$ and the bimodule Segre embedding, which we construct. Truncating a truncated family of point modules of length $i+1$ by taking its first $i$ components defines a morphism $\Gamma_{i} \rightarrow \Gamma_{i-1}$ which makes the set $\{\Gamma_{n}\}$ an inverse system. In order for the point modules of $T(\mathcal{E})/\mathcal{I}$ to be parameterizable by a scheme, this system must be eventually constant. In [\textbf{20}], we give sufficient conditions for this system to be constant and show that these conditions are satisfied when ${\mathsf{Proj}} T(\mathcal{E})/\mathcal{I}$ is a quantum ruled surface. In this case, we show the point modules over $T(\mathcal{E})/\mathcal{I}$ are parameterized by the closed points of ${\mathbb{P}}_{X^{2}}(\mathcal{E})$.
Gromov Hausdorff Distance For Quantum Metric Spaces
DOWNLOAD
Author : Marc Aristide Rieffel
language : en
Publisher:
Release Date : 2004
Gromov Hausdorff Distance For Quantum Metric Spaces written by Marc Aristide Rieffel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Noncommutative Geometry And Optimal Transport
DOWNLOAD
Author : Pierre Martinetti
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-26
Noncommutative Geometry And Optimal Transport written by Pierre Martinetti and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-26 with Mathematics categories.
The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffel's observation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.
Operator Algebras And Their Applications
DOWNLOAD
Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-07-28
Operator Algebras And Their Applications written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-28 with Mathematics categories.
his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.
Quanta Of Maths
DOWNLOAD
Author : Institut des hautes études scientifiques (Paris, France)
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Quanta Of Maths written by Institut des hautes études scientifiques (Paris, France) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.
Superstrings Geometry Topology And C Algebras
DOWNLOAD
Author : Robert S. Doran
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-10-13
Superstrings Geometry Topology And C Algebras written by Robert S. Doran and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-13 with Mathematics categories.
This volume contains the proceedings of an NSF-CBMS Conference held at Texas Christian University in Fort Worth, Texas, May 18-22, 2009. The papers, written especially for this volume by well-known mathematicians and mathematical physicists, are an outgrowth of the talks presented at the conference. Topics examined are highly interdisciplinary and include, among many other things, recent results on D-brane charges in $K$-homology and twisted $K$-homology, Yang-Mills gauge theory and connections with non-commutative geometry, Landau-Ginzburg models, $C^*$-algebraic non-commutative geometry and ties to quantum physics and topology, the rational homotopy type of the group of unitary elements in an Azumaya algebra, and functoriality properties in the theory of $C^*$-crossed products and fixed point algebras for proper actions. An introduction, written by Jonathan Rosenberg, provides an instructive overview describing common themes and how the various papers in the volume are interrelated and fit together. The rich diversity of papers appearing in the volume demonstrates the current interplay between superstring theory, geometry/topology, and non-commutative geometry. The book will be of interest to graduate students, mathematicians, mathematical physicists, and researchers working in these areas.
Riesz Transforms Hodge Dirac Operators And Functional Calculus For Multipliers
DOWNLOAD
Author : Cédric Arhancet
language : en
Publisher: Springer Nature
Release Date : 2022-05-05
Riesz Transforms Hodge Dirac Operators And Functional Calculus For Multipliers written by Cédric Arhancet and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-05 with Mathematics categories.
This book on recent research in noncommutative harmonic analysis treats the Lp boundedness of Riesz transforms associated with Markovian semigroups of either Fourier multipliers on non-abelian groups or Schur multipliers. The detailed study of these objects is then continued with a proof of the boundedness of the holomorphic functional calculus for Hodge–Dirac operators, thereby answering a question of Junge, Mei and Parcet, and presenting a new functional analytic approach which makes it possible to further explore the connection with noncommutative geometry. These Lp operations are then shown to yield new examples of quantum compact metric spaces and spectral triples. The theory described in this book has at its foundation one of the great discoveries in analysis of the twentieth century: the continuity of the Hilbert and Riesz transforms on Lp. In the works of Lust-Piquard (1998) and Junge, Mei and Parcet (2018), it became apparent that these Lp operations can be formulated on Lp spaces associated with groups. Continuing these lines of research, the book provides a self-contained introduction to the requisite noncommutative background. Covering an active and exciting topic which has numerous connections with recent developments in noncommutative harmonic analysis, the book will be of interest both to experts in no-commutative Lp spaces and analysts interested in the construction of Riesz transforms and Hodge–Dirac operators.
Noncommutative Cosmology
DOWNLOAD
Author : Marcolli Matilde
language : en
Publisher: World Scientific
Release Date : 2017-12-26
Noncommutative Cosmology written by Marcolli Matilde and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-26 with Science categories.
Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal structures in cosmology. Relations between noncommutative and algebro-geometric methods in cosmology is also discussed, including the occurrence of motives, periods, and modular forms in spectral models of gravity. Contents: PrefaceAcknowledgmentsGravity and Matter in Noncommutative GeometryRenormalization Group Flows and Early Universe ModelsCosmic TopologyAlgebro-geometric Models in CosmologyMixmaster CosmologiesThe Spectral Action on Bianchi IX CosmologiesFractal and Multifractal Structures in CosmologyNoncommutative Quantum CosmologyBibliography Readership: Graduate students and researchers in mathematical physics and theoretical cosmology. Keywords: Cosmology;Gravity;Particle Physics;GeometryReview: Key Features: While there are recent books that focus on applications of noncommutative geometry to particle physics models, there is presently no other book that focuses on applications to cosmology