Methods Of Noncommutative Geometry For Group C Algebras
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Methods Of Noncommutative Geometry For Group C Algebras
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Author : Do Ngoc Diep
language : en
Publisher: CRC Press
Release Date : 1999-12-06
Methods Of Noncommutative Geometry For Group C Algebras written by Do Ngoc Diep and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-06 with Mathematics categories.
The description of the structure of group C*-algebras is a difficult problem, but relevant to important new developments in mathematics, such as non-commutative geometry and quantum groups. Although a significant number of new methods and results have been obtained, until now they have not been available in book form. This volume provides an introduction to and presents research on the study of group C*-algebras, suitable for all levels of readers - from graduate students to professional researchers. The introduction provides the essential features of the methods used. In Part I, the author offers an elementary overview - using concrete examples-of using K-homology, BFD functors, and KK-functors to describe group C*-algebras. In Part II, he uses advanced ideas and methods from representation theory, differential geometry, and KK-theory, to explain two primary tools used to study group C*-algebras: multidimensional quantization and construction of the index of group C*-algebras through orbit methods. The structure of group C*-algebras is an important issue both from a theoretical viewpoint and in its applications in physics and mathematics. Armed with the background, tools, and research provided in Methods of Noncommutative Geometry for Group C*-Algebras, readers can continue this work and make significant contributions to perfecting the theory and solving this problem.
Non Commutative Geometry Methods For Group C Algebras
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Author : Do Ngoc Diep
language : en
Publisher:
Release Date : 1999-02-01
Non Commutative Geometry Methods For Group C Algebras written by Do Ngoc Diep and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-01 with categories.
Abstract And Applied Analysis Proceedings Of The International Conference
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Author : Nguyen Minh Chuong
language : en
Publisher: World Scientific
Release Date : 2004-06-01
Abstract And Applied Analysis Proceedings Of The International Conference written by Nguyen Minh Chuong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-01 with Mathematics categories.
This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material — the coefficients may jump from domain to domain; Stochastic Analysis — many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Abstract And Applied Analysis
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Author : N. M. Chuong
language : en
Publisher: World Scientific
Release Date : 2004
Abstract And Applied Analysis written by N. M. Chuong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with History categories.
This volume takes up various topics in Mathematical Analysis including boundary and initial value problems for Partial Differential Equations and Functional Analytic methods.Topics include linear elliptic systems for composite material ? the coefficients may jump from domain to domain; Stochastic Analysis ? many applied problems involve evolution equations with random terms, leading to the use of stochastic analysis.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences
Basic Noncommutative Geometry
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Author : Masoud Khalkhali
language : en
Publisher: European Mathematical Society
Release Date : 2009
Basic Noncommutative Geometry written by Masoud Khalkhali and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.
Noncommutative Geometry And Representation Theory In Mathematical Physics
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Author : Jürgen Fuchs
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Noncommutative Geometry And Representation Theory In Mathematical Physics written by Jürgen Fuchs 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 2005 with Mathematics categories.
Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influentialin physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities. This volume contains the plenary talks fromthe international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics. The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitablefor graduate students and researchers interested in mathematical physics.
Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics
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Author : Kar Ping Shum
language : en
Publisher: World Scientific
Release Date : 2008-06-17
Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics written by Kar Ping Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-17 with Mathematics categories.
This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.
Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics
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Author : K. P. Shum
language : en
Publisher: World Scientific
Release Date : 2008
Advances In Algebra And Combinatorics Proceedings Of The Second International Congress In Algebra And Combinatorics written by K. P. Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.
Twenty Years Of Bialowieza A Mathematical Anthology Aspects Of Differential Geometric Methods In Physics
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Author : S Twareque Ali
language : en
Publisher: World Scientific
Release Date : 2005-01-27
Twenty Years Of Bialowieza A Mathematical Anthology Aspects Of Differential Geometric Methods In Physics written by S Twareque Ali and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-27 with Science categories.
This volume marks the twentieth anniversary of the Bialowieza series of meetings on Differential Geometric Methods in Physics; the anniversary meeting was held during July 1-7, 2001. The Bialowieza meetings, held every year during the first week of July, have now grown into an annual pilgrimage for an international group of physicists and mathematicians. The topics discussed at the meetings, while within the broad area of differential geometric methods in physics, have focused around quantization, coherent states, infinite dimensional systems, symplectic geometry, spectral theory and harmonic analysis. The present volume brings together a set of specially invited papers from leading experts in the various fields, who have contributed to these meetings and whose work represents a cross-section of the topics discussed. Consequently, rather than a proceedings volume, this book embodies the spirit of the Bialowieza workshops and reflects their scientific tenor, as a tribute to the completion of two decades of a shared scientific experience.This book will be of interest to researchers and graduate students working in the area of differential geometric methods in physics, as it gives interesting glimpses into the present state of the art from different points of view.
Noncommutative Geometry And Optimal Transport
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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.