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Quantum Groups And Noncommutative Geometry
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Book Synopsis Quantum Groups and Noncommutative Geometry by : Yuri I. Manin
Download or read book Quantum Groups and Noncommutative Geometry written by Yuri I. Manin and published by Springer. This book was released on 2018-10-11 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Manin systematically develops an approach to quantum groups as symmetry objects in noncommutative geometry in contrast to the more deformation-oriented approach due to Faddeev, Drinfeld, and others. This new edition contains an extra chapter by Theo Raedschelders and Michel Van den Bergh, surveying recent work that focuses on the representation theory of a number of bi- and Hopf algebras that were first introduced in Manin's lectures, and have since gained a lot of attention. Emphasis is placed on the Tannaka–Krein formalism, which further strengthens Manin's approach to symmetry and moduli-objects in noncommutative geometry.
Book Synopsis Quantum Groups and Noncommutative Spaces by : Matilde Marcolli
Download or read book Quantum Groups and Noncommutative Spaces written by Matilde Marcolli and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.
Book Synopsis Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions by : Daniel Kastler
Download or read book Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions written by Daniel Kastler and published by . This book was released on 1999 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents include: Hochschild Homology of Function Algebras Associated with Singularities; On the KK-Theory of Stable Projective Limits; Noncommutative Integrability; Gauge Invariance of the Chern-Simons Action in Noncommutative Geometry; The Analysis of the Hochshild Homology; Coproducts and Operations on Cyclic Cohomology; Powers of Quantum Matrices and Relations Between Them; Introductory Notes on Extensions of Hopf Algebras; Hopf Algebras from the Quantum Geometry Point of View; Equation Pentagonale, Bige bres et Espaces de Modules; Chiral Anomalies in the Spectral Action; Standard Model and Unimodularity Condition; On Feynman Graphs as Elements of a Hopf Algebra.
Book Synopsis Topics in Non-Commutative Geometry by : Y. Manin
Download or read book Topics in Non-Commutative Geometry written by Y. Manin and published by Princeton University Press. This book was released on 2014-07-14 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Groups and Non-commutative Geometry by : Jurij I. Manin
Download or read book Quantum Groups and Non-commutative Geometry written by Jurij I. Manin and published by Centre De Recherches Mathematiques. This book was released on 1988 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Noncommutative Geometry and Quantum Groups by : Piotr M. Hajac
Download or read book Noncommutative Geometry and Quantum Groups written by Piotr M. Hajac and published by . This book was released on 2003 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Groups and Noncommutative Geometry by : Shahn Majid
Download or read book Quantum Groups and Noncommutative Geometry written by Shahn Majid and published by . This book was released on 2004 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Isometry Groups by : Debashish Goswami
Download or read book Quantum Isometry Groups written by Debashish Goswami and published by Springer. This book was released on 2017-01-05 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an up-to-date overview of the recently proposed theory of quantum isometry groups. Written by the founders, it is the first book to present the research on the “quantum isometry group”, highlighting the interaction of noncommutative geometry and quantum groups, which is a noncommutative generalization of the notion of group of isometry of a classical Riemannian manifold. The motivation for this generalization is the importance of isometry groups in both mathematics and physics. The framework consists of Alain Connes’ “noncommutative geometry” and the operator-algebraic theory of “quantum groups”. The authors prove the existence of quantum isometry group for noncommutative manifolds given by spectral triples under mild conditions and discuss a number of methods for computing them. One of the most striking and profound findings is the non-existence of non-classical quantum isometry groups for arbitrary classical connected compact manifolds and, by using this, the authors explicitly describe quantum isometry groups of most of the noncommutative manifolds studied in the literature. Some physical motivations and possible applications are also discussed.
Book Synopsis Methods of Noncommutative Geometry for Group C*-Algebras by : Do Ngoc Diep
Download or read book Methods of Noncommutative Geometry for Group C*-Algebras written by Do Ngoc Diep and published by CRC Press. This book was released on 1999-12-06 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Book Synopsis Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups by : Ludwig Pittner
Download or read book Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups written by Ludwig Pittner and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum groups and quantum algebras as well as non-commutative differential geometry are important in mathematics and considered to be useful tools for model building in statistical and quantum physics. This book, addressing scientists and postgraduates, contains a detailed and rather complete presentation of the algebraic framework. Introductory chapters deal with background material such as Lie and Hopf superalgebras, Lie super-bialgebras, or formal power series. Great care was taken to present a reliable collection of formulae and to unify the notation, making this volume a useful work of reference for mathematicians and mathematical physicists.
Book Synopsis Quantum Groups and Noncommutative Geometry by :
Download or read book Quantum Groups and Noncommutative Geometry written by and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Noncommutative Structures in Mathematics and Physics by : S. Duplij
Download or read book Noncommutative Structures in Mathematics and Physics written by S. Duplij and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.
Book Synopsis Advances in Noncommutative Geometry by : Ali Chamseddine
Download or read book Advances in Noncommutative Geometry written by Ali Chamseddine and published by Springer Nature. This book was released on 2020-01-13 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.
Book Synopsis Perspectives on Noncommutative Geometry by : Masoud Khalkhali
Download or read book Perspectives on Noncommutative Geometry written by Masoud Khalkhali and published by American Mathematical Soc.. This book was released on 2011 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008. Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture. Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples. Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume. This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.
Book Synopsis Structural Aspects Of Quantum Field Theory (In 2 Volumes) by : Gerhard Grensing
Download or read book Structural Aspects Of Quantum Field Theory (In 2 Volumes) written by Gerhard Grensing and published by World Scientific. This book was released on 2013-05-21 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.
Book Synopsis An Invitation to Noncommutative Geometry by : Masoud Khalkhali
Download or read book An Invitation to Noncommutative Geometry written by Masoud Khalkhali and published by World Scientific. This book was released on 2008 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
