Topics In Noncommutative Geometry
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Topics In Non Commutative Geometry
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Author : Yuri I. Manin
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Topics In Non Commutative Geometry written by Yuri I. Manin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces." Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Topics In Noncommutative Geometry
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Author : Guillermo Cortiñas
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Topics In Noncommutative Geometry written by Guillermo Cortiñas 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 2012 with Mathematics categories.
Luis Santalo Winter Schools are organized yearly by the Mathematics Department and the Santalo Mathematical Research Institute of the School of Exact and Natural Sciences of the University of Buenos Aires (FCEN). This volume contains the proceedings of the third Luis Santalo Winter School which was devoted to noncommutative geometry and held at FCEN July 26-August 6, 2010. Topics in this volume concern noncommutative geometry in a broad sense, encompassing various mathematical and physical theories that incorporate geometric ideas to the study of noncommutative phenomena. It explores connections with several areas including algebra, analysis, geometry, topology and mathematical physics. Bursztyn and Waldmann discuss the classification of star products of Poisson structures up to Morita equivalence. Tsygan explains the connections between Kontsevich's formality theorem, noncommutative calculus, operads and index theory. Hoefel presents a concrete elementary construction in operad theory. Meyer introduces the subject of $\mathrm{C}^*$-algebraic crossed products. Rosenberg introduces Kasparov's $KK$-theory and noncommutative tori and includes a discussion of the Baum-Connes conjecture for $K$-theory of crossed products, among other topics. Lafont, Ortiz, and Sanchez-Garcia carry out a concrete computation in connection with the Baum-Connes conjecture. Zuk presents some remarkable groups produced by finite automata. Mesland discusses spectral triples and the Kasparov product in $KK$-theory. Trinchero explores the connections between Connes' noncommutative geometry and quantum field theory. Karoubi demonstrates a construction of twisted $K$-theory by means of twisted bundles. Tabuada surveys the theory of noncommutative motives.
Topics In Noncommutative Geometry
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Author : I͡U. I. Manin
language : en
Publisher:
Release Date : 1991
Topics In Noncommutative Geometry written by I͡U. I. Manin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application of commutative algebra cannot be used to describe geometric objects, emphasizing the recent upsurge of activity in studying noncommutative rings as if they were function rings on "noncommutative spaces." Manin begins by summarizing and giving examples of some of the ideas that led to the new concepts of noncommutative geometry, such as Connes' noncommutative de Rham complex, supergeometry, and quantum groups. He then discusses supersymmetric algebraic curves that arose in connection with superstring theory; examines superhomogeneous spaces, their Schubert cells, and superanalogues of Weyl groups; and provides an introduction to quantum groups. This book is intended for mathematicians and physicists with some background in Lie groups and complex geometry. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Noncommutative Geometry Arithmetic And Related Topics
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Author : Caterina Consani
language : en
Publisher: JHU Press
Release Date : 2011
Noncommutative Geometry Arithmetic And Related Topics written by Caterina Consani and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.
An Invitation To Noncommutative Geometry
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Author : Matilde Marcolli
language : en
Publisher: World Scientific
Release Date : 2008-02-11
An Invitation To Noncommutative Geometry written by Matilde Marcolli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-11 with Science categories.
This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory.
Topics In Algebraic And Noncommutative Geometry
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Author : Ruth Ingrid Michler
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Topics In Algebraic And Noncommutative Geometry written by Ruth Ingrid Michler 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 2003 with Mathematics categories.
This book presents the proceedings of two conferences, Resolution des singularites et geometrie non commutative and the Annapolis algebraic geometry conference. Research articles in the volume cover various topics of algebraic geometry, including the theory of Jacobians, singularities, applications to cryptography, and more. The book is suitable for graduate students and research mathematicians interested in algebraic geometry.
Noncommutative Algebraic Geometry And Representations Of Quantized Algebras
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Author : A. Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Noncommutative Algebraic Geometry And Representations Of Quantized Algebras written by A. Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book is based on lectures delivered at Harvard in the Spring of 1991 and at the University of Utah during the academic year 1992-93. Formally, the book assumes only general algebraic knowledge (rings, modules, groups, Lie algebras, functors etc.). It is helpful, however, to know some basics of algebraic geometry and representation theory. Each chapter begins with its own introduction, and most sections even have a short overview. The purpose of what follows is to explain the spirit of the book and how different parts are linked together without entering into details. The point of departure is the notion of the left spectrum of an associative ring, and the first natural steps of general theory of noncommutative affine, quasi-affine, and projective schemes. This material is presented in Chapter I. Further developments originated from the requirements of several important examples I tried to understand, to begin with the first Weyl algebra and the quantum plane. The book reflects these developments as I worked them out in reallife and in my lectures. In Chapter 11, we study the left spectrum and irreducible representations of a whole lot of rings which are of interest for modern mathematical physics. The dasses of rings we consider indude as special cases: quantum plane, algebra of q-differential operators, (quantum) Heisenberg and Weyl algebras, (quantum) enveloping algebra ofthe Lie algebra sl(2) , coordinate algebra of the quantum group SL(2), the twisted SL(2) of Woronowicz, so called dispin algebra and many others.
Noncommutative Cosmology
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Author : Matilde Marcolli
language : en
Publisher: World Scientific
Release Date : 2017-12-26
Noncommutative Cosmology written by Matilde Marcolli 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.
Elements Of Noncommutative Geometry
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Author : Jose M. Gracia-Bondia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Elements Of Noncommutative Geometry written by Jose M. Gracia-Bondia and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Topics In Cyclic Theory
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Author : Daniel G. Quillen
language : en
Publisher: Cambridge University Press
Release Date : 2020-07-09
Topics In Cyclic Theory written by Daniel G. Quillen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-09 with Mathematics categories.
This accessible introduction for Ph.D. students and non-specialists provides Quillen's unique development of cyclic theory.