Noncommutative geometry and representation theory in mathematical physics

satellite conference to the Fourth European Congress of Mathematics, July 5-10, 2004, Karlstad University, Karlstad, Sweden

Publisher: American Mathematical Society in Providence, R.I

Written in English
Published: Pages: 384 Downloads: 357
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Subjects:

  • Noncommutative differential geometry -- Congresses.,
  • Representations of groups -- Congresses.,
  • Mathematical physics -- Congresses.

Edition Notes

Includes bibliographical references.

StatementJürgen Fuchs ... [et al.] editors.
GenreCongresses.
SeriesContemporary mathematics -- 391, Contemporary mathematics (American Mathematical Society) -- v. 391.
ContributionsFuchs, Jürgen, 1957 May 19-, European Congress of Mathematics (4th : 2004 : Karlstad, Sweden)
Classifications
LC ClassificationsQC20.7.D52 N666 2005
The Physical Object
Paginationxiv, 384 p. :
Number of Pages384
ID Numbers
Open LibraryOL22730592M
ISBN 100821837184

The lecture notes of this course at the EMS Summer School on Noncommutative Geometry and Applications in September, are now published by the EMS. Here are the contents, preface and updated bibliography from the published book. Contents 1 Commutative Geometry from the Noncommutative Point of View The Gelfand–Na˘ımark cofunctors.   Noncommutative geometry and Quantum physics on manifolds with boundary T.R. Govindarajan Chennai Mathematical Institute, Chennai Quantum theory on manifolds with boundary present novel features due to boundary conditions. There are edge states localised at the boundary. Noncommutative rings resemble rings of matrices in many respects. Following the model of algebraic geometry, attempts have been made recently at defining noncommutative geometry based on noncommutative rings. Noncommutative rings and associative algebras (rings that are also vector spaces) are often studied via their categories of modules. A module over a ring is an abelian group . "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.

Objectives This is the third Shanghai workshop on Noncommutative Algebraic geometry. The conference emphasizes on most significant developments, new research directions and interactions with other fields such as noncommutative algebra, representation theory, algebraic geometry, and mathematical physics. PDF | The structure of a manifold can be encoded in the commutative algebra of functions on the manifold it self - this is usual -. In the case of a non | Find, read and cite all the research. Lecture Febru Introduction to spectral triples in noncommutative geometry, real structures, Morita equivalence and inner fluctuations, the Left-Right symmetric algebra Lecture Febru Odd bimodules, representations of the left-right symmetric algebra, generations and particles as basis elements, real structure and. I took a course last year on noncommutative geometry (which kind of turned out to be a whole lot of homological algebra). I get that we want to come up with some sort of geometric perspective on noncommutative rings and algebras like we have for commutative ones ({commutative rings} {affine schemes}, {commutative C*-algebras} {compact Hausdorff spaces}), and that at the moment.

Noncommutative geometry and representation theory in mathematical physics Download PDF EPUB FB2

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.

From the foreword to the book: "Deeply rooted in the modern theory of operator algebras and inspired by two of the most influential mathematical discoveries of the 20th century, the foundations of quantum mechanics and the index theory, Connes' vision of noncommutative geometry echoes the astonishing anticipation of Riemann that ''it is quite conceivable that the metric relations of space in.

Measure theory (Chapters I and V) 8 2. Topology and K-theory (Chapter II) 14 3. Cyclic cohomology (Chapter III) 19 4. The quantized calculus (Chapter IV) 25 5. The metric aspect of noncommutative geometry 34 Chapter 1. Noncommutative Spaces and Measure Theory 39 1. Heisenberg and the Noncommutative Algebra of Physical Quantities 40 2.

Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two volume contains the plenary talks from the international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad.

Noncommutative geometry and representation theory in mathematical physics; proceedings. Satellite conference to the Fourth European Congress of Mathematics ( Karlstad, Sweden) Ed.

by Jurgen Fuchs et al. Download The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann.

His research specialties include noncommutative geometry, mathematical physics, noncommutative spectral geometry, cyclic cohomology, quantum groups and Hopf algebras. Noncommutative geometry and representation theory in mathematical physics book Henri Moscovici is professor and Alice Woods Chair in Mathematics at Ohio State University.

His areas of research include noncommutative geometry, global analysis and. Basic Noncommutative Geometry. Well, finally BNCG is published now.

You can check its cover here. The book is published by the European Mathematical Society Publishing House. Happy holidays to everyone. Posted by Masoud Khalkhali at AM 3 comments: Wednesday, October 7, There are many ways to compute this invariants, and some of them come straight out of noncommutative geometry.

See "Disordered topological insulators: a non-commutative geometry perspective" by Emil Prodan, in Journal of Physics A: Mathematical and Theoretical, 44(), Get this from a library. Noncommutative geometry and representation theory in mathematical physics: satellite conference to the Fourth European Congress of Mathematics, July, Karlstad University, Karlstad, Sweden.

[Jürgen Fuchs;]. This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes.

Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of.

The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Cited by: Algebraic Geometry, Representation Theory.

I am interested in the interface between representation theory, algebraic geometry and mathematical physics. One focus of my current research is a new approach, joint with David Nadler to the representation theory of real and complex Lie groups built from a combination of the geometric Langlands.

The book is the first full-size Encyclopedia which simultaneously covers such well-established and modern subjects as quantum field theory, supersymmetry, supergravity, M-theory, black holes and quantum gravity, noncommutative geometry, representation theory, categories and quantum groups, and their : $ Book Description.

Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics.

The American Mathematical Monthly; Mathematics Magazine; The College Mathematics Journal; Loci/JOMA. Browse; How to Cite; Communications in Visual Mathematics; Convergence. About Convergence; What's in Convergence. Convergence Articles; Images for Classroom Use.

Mathematical Treasures; Portrait Gallery; Paul R. Halmos Photograph Collection. About this book Introduction 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.

This textbook presents an expanded write-up of Manin's celebrated Montreal author 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. Rosenberg A.L. () Noncommutative Local Algebra and Representations of certain rings of mathematical physics.

In: Noncommutative Algebraic Geometry and Representations of Quantized Algebras. Mathematics and Its Applications, vol Author: Alexander L. Rosenberg. Noncommutative Geometry and Representation Theory in Mathematical Physics About this Title.

Jürgen Fuchs, Jouko Mickelsson, Grigori Rozenblioum, Alexander Stolin and Anders Westerberg, Editors. Publication: Contemporary Mathematics Publication Year Volume ISBNs: (print); (online). Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry.

This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics.

Noncommutative Geometry and Representation Theory in Mathematical Physics: Proceedings. Infinite-dimensional aspects of representation theory and applications; proceedings. Commutative algebra and algebraic geometry; proceedings. Advanced Summer School in Physics: Frontiers in Contemporary Physics; Proceedings.

Noncommutative geometry and representation theory in mathematical physics. Papers from the Satellite Conference to the 4th European Congress of Mathematics held at Karlstad University, Karlstad, July 5- Author: Grigori Rozenblioum, Alexander Stolin, Youko Mickelson, Jurgen Fuchs, Anders Westerberg.

light of noncommutative geometry, the issue of \observables" in gravity and our joint work with Ali Chamseddine on the spectral action, with a flrst attempt to write down a functional integral on the space of noncommutative geometries.

Contents 1. Introduction 1 2. Lessons from renormalization 4 3. Noncommutative Geometry 11 The book is the first full-size Encyclopedia which simultaneously covers such well-established and modern subjects as quantum field theory, supersymmetry, supergravity, M-theory, black holes and quantum gravity, noncommutative geometry, representation theory, categories and quantum groups, and their generalizations.

Welcome to the Non-Commutative Geometry group at the University of Copenhagen Our group carries out research in non-commutative geometry and operator algebras. Our interests include index theory, non-commutative manifolds, C*-algebras, von Neumann algebras, Banach algebras, and symbolic dynamical systems.

On anomalies and noncommutative geometry. Methods of modern mathematical physics. 1: Functional analysis (There is also a close connection with the representation theory of infinite.

The Mathematical Sciences Research Institute (MSRI), founded inis an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions. The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the.

Noncommutative geometry, quantum fields and motives / Alain Connes, Matilde Marcolli. — (Colloquium publications (American Mathematical Society), ISSN ; v. 55) Includes bibliographical references and index.

ISBN (alk. paper) 1. Noncommutative differential geometry. Quantum field theory, I. Marcolli. Many results about the representation theory of G follow quickly by applying the Artin-Wedderburn Theorem to the group ring C[G].

(Of course, first you need to prove Maschke's Theorem, which tells you that C[G] is semisimple.) Also, one of the reasons that commutative algebra is so important is because you can use commutative rings to do geometry.

Noncommutative geometry is a novel approach which is opening up new possibilities for geometry from a mathematical viewpoint. It is also providing new tools for the investigation of quantum space-time in physics.

Recent developments in string theory have supported the idea of quantum spaces, and have strongly stimulated the research in this field.Noncommutative geometry Alain Connes This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes.I am interested in the interface between representation theory, algebraic geometry and mathematical physics.

One focus of my current research is a new approach, joint with David Nadler to the representation theory of real and complex Lie groups built from a combination of the geometric Langlands program, topological field theory and derived algebraic geometry.