Quantum Groups And Non Commutative Geometry PDF Download
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Author | : Yuri I. Manin |
Publisher | : Springer |
Total Pages | : 125 |
Release | : 2018-10-11 |
Genre | : Mathematics |
ISBN | : 3319979876 |
Download Quantum Groups and Noncommutative Geometry Book in PDF, ePub and Kindle
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.
Author | : Matilde Marcolli |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2010-11-02 |
Genre | : Mathematics |
ISBN | : 3834898317 |
Download Quantum Groups and Noncommutative Spaces Book in PDF, ePub and Kindle
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.
Author | : Y. Manin |
Publisher | : Princeton University Press |
Total Pages | : 173 |
Release | : 2014-07-14 |
Genre | : Mathematics |
ISBN | : 1400862515 |
Download Topics in Non-Commutative Geometry Book in PDF, ePub and Kindle
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.
Author | : Jurij I. Manin |
Publisher | : Centre De Recherches Mathematiques |
Total Pages | : 91 |
Release | : 1988 |
Genre | : Algebra - Asociativne algebre - Nekomutativna geometrija |
ISBN | : 9782921120005 |
Download Quantum Groups and Non-commutative Geometry Book in PDF, ePub and Kindle
Author | : Daniel Kastler |
Publisher | : |
Total Pages | : 490 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : |
Download Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions Book in PDF, ePub and Kindle
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.
Author | : Alain Connes |
Publisher | : Springer |
Total Pages | : 364 |
Release | : 2003-12-15 |
Genre | : Mathematics |
ISBN | : 3540397027 |
Download Noncommutative Geometry Book in PDF, ePub and Kindle
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.
Author | : Ali Chamseddine |
Publisher | : Springer Nature |
Total Pages | : 753 |
Release | : 2020-01-13 |
Genre | : Mathematics |
ISBN | : 3030295974 |
Download Advances in Noncommutative Geometry Book in PDF, ePub and Kindle
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.
Author | : Do Ngoc Diep |
Publisher | : CRC Press |
Total Pages | : 4 |
Release | : 1999-12-06 |
Genre | : Mathematics |
ISBN | : 9781584880196 |
Download Methods of Noncommutative Geometry for Group C*-Algebras Book in PDF, ePub and Kindle
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.
Author | : Piotr M. Hajac |
Publisher | : |
Total Pages | : 356 |
Release | : 2003 |
Genre | : Harmonic analysis |
ISBN | : |
Download Noncommutative Geometry and Quantum Groups Book in PDF, ePub and Kindle
Author | : Ludwig Pittner |
Publisher | : Springer Science & Business Media |
Total Pages | : 476 |
Release | : 2009-01-29 |
Genre | : Science |
ISBN | : 3540478019 |
Download Algebraic Foundations of Non-Commutative Differential Geometry and Quantum Groups Book in PDF, ePub and Kindle
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.