Noncommutative geometry and quantum groups

Noncommutative geometry and quantum groups Download PDF EPUB FB2

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.

Quantum Groups and Noncommutative Geometry Yuri I. Manin This textbook presents the second edition of Manin's celebrated Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups.

Quantum groups and noncommutative geometry | Y. Manin | Noncommutative geometry and quantum groups book | B–OK. Download books for free. Find books. The subject of noncommutative geometry has recently made its way into theoretical physics, and so a perusal of this book would be of interest to individuals working in string theory or quantum field theory.

The main idea of this book is to generalize measure and operator theory to non-commutative situations.4/5(9). Title: Quantum Groups and Noncommutative Geometry. Authors: S. Majid. Download PDF Abstract: Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself powerful enough to Cited by: Noncommutative Geometry and Quantum Group Symmetries candidate Francesco D’Andrea supervisors external referees Prof.

Ludwik Dabrowski, Prof. Marc A. Rieffel Prof. Giovanni LandiProf. Joseph C. V arilly arXivv1 [] 19 Nov Cited by: 2. space in quantum mechanics but there are many others, such as the leaf spaces of foliations, duals of nonabelian discrete groups, the space of Penrose tilings, the noncommutative torus which plays a role in M-theory compactification, and finally the space of Q.

and basic idea of algebraic geometry. The purpose of this book is to extend this correspondence to the noncommutative case in the framework of real analysis. The theory, called noncommutative geometry, rests on two essential points: 1. The existence of many natural spaces for which the classical set-theoretic tools.

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 by: 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 by: Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry (Aspects of Mathematics Book 41) - Kindle edition by Matilde Marcolli, Deepak Parashar.

Download it once and read it on your Kindle device, PC, phones or tablets. Genre/Form: Conference papers and proceedings Congresses: Additional Physical Format: Online version: Noncommutative geometry and quantum groups. Warszawa: Institute of Mathematics, Polish Academy of Sciences, QUANTUM GROUPS AND NONCOMMUTATIVE GEOMETRY Shahn Majid School of Mathematical Sciences, Queen Mary and West eld College University of London, Mile End Rd, London E1 4NS, UK November, Abstract Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certainFile Size: KB.

Quantum Groups and Noncommutative Geometry Article (PDF Available) in Journal of Mathematical Physics 41(6) June with Reads How we measure 'reads'Author: S. Majid.

Downloads Books. Noncommutative Geometry MB. Academic Press, San Diego, CA,p., ISBN X. Noncommutative Geometry, Quantum Fields and Motives MB. With Matilde Marcolli. Quantum group Symmetries and the Local Index Formula for SU q (2) KB KB.

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.

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.

Conformal Manifolds. Fredholm Modules and Rank-One Discrete Groups. Elliptic Theory on the Noncommutative Torus (NOTE: See book for proper symbol. Math T with a 2 over and the Quantum Hall Effect. Entire Cyclic Cohomology.

The Chern Character of (-Summable Fredholm Modules. (-Summable K-Cycles, Discrete Groups, and Quantum Field Theory. This is a monograph on the noncommutative generalisation of Riemannian geometry. It covers topics such as Hopf algebras, cyclic cohomology, as well as noncommutative analogues of complex structures and Riemannian geometry.

There are applications to physics in the form of quantum spacetime. His textbook Foundations of Quantum Group Theory is a standard text still used by researchers today. He also pioneered a quantum groups approach to noncommutative geometry and the use of such methods as a route to quantum gravity, leading in to the first model with testable predictions of quantum al advisor: Clifford Taubes, Arthur Jaffe.

Conformal Manifolds. Fredholm Modules and Rank-One Discrete Groups. Elliptic Theory on the Noncommutative Torus (NOTE: See book for proper symbol.

Math T with a 2 over and the Quantum Hall Effect. Entire Cyclic Cohomology. The Chern Character of (-Summable Fredholm Modules. (-Summable K-Cycles, Discrete Groups, and Quantum Field Theory/5(7).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.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.