Quantum Groups Non Commutative Differential Geometry And Applications

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Genre :
Author : Peter Schupp
Publisher :
Release : 1993
File : 312 Pages
ISBN-13 : UCAL:C3374511


An Introduction To Noncommutative Differential Geometry And Its Physical Applications

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A thoroughly revised introduction to non-commutative geometry.

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Genre : Mathematics
Author : J. Madore
Publisher : Cambridge University Press
Release : 1999-06-24
File : 381 Pages
ISBN-13 : 9780521659918


Algebraic Foundations Of Non Commutative Differential Geometry And Quantum Groups

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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.

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Genre : Science
Author : Ludwig Pittner
Publisher : Springer Science & Business Media
Release : 2009-01-29
File : 476 Pages
ISBN-13 : 9783540478010


Noncommutative Differential Geometry And Its Applications To Physics

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Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

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Genre : Science
Author : Yoshiaki Maeda
Publisher : Springer Science & Business Media
Release : 2012-12-06
File : 310 Pages
ISBN-13 : 9789401007047


Quantum Groups And Noncommutative Spaces

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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.

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Genre : Mathematics
Author : Matilde Marcolli
Publisher : Springer Science & Business Media
Release : 2010-11-02
File : 247 Pages
ISBN-13 : 9783834898319


Quantum Groups And Their Representations

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This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.

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Genre : Science
Author : Anatoli Klimyk
Publisher : Springer Science & Business Media
Release : 2012-12-06
File : 568 Pages
ISBN-13 : 9783642608964


Noncommutative Geometry And Global Analysis

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This volume represents the proceedings of the conference on Noncommutative Geometric Methods in Global Analysis, held in honor of Henri Moscovici, from June 29-July 4, 2009, in Bonn, Germany. Henri Moscovici has made a number of major contributions to noncommutative geometry, global analysis, and representation theory. This volume, which includes articles by some of the leading experts in these fields, provides a panoramic view of the interactions of noncommutative geometry with a variety of areas of mathematics. It focuses on geometry, analysis and topology of manifolds and singular spaces, index theory, group representation theory, connections of noncommutative geometry with number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.

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Genre : Mathematics
Author : Henri Moscovici
Publisher : American Mathematical Soc.
Release : 2011
File : 337 Pages
ISBN-13 : 9780821849446


Scientific And Technical Aerospace Reports

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Genre : Aeronautics
Author :
Publisher :
Release : 1994
File : 328 Pages
ISBN-13 : MINN:30000011064577


An Introduction To Noncommutative Spaces And Their Geometries

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These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content. This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.

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Genre : Science
Author : Giovanni Landi
Publisher : Springer Science & Business Media
Release : 2003-07-01
File : 216 Pages
ISBN-13 : 9783540149491


Algebras Rings And Modules

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Presenting an introduction to the theory of Hopf algebras, the authors also discuss some important aspects of the theory of Lie algebras. This book includes a chapters on the Hopf algebra of symmetric functions, the Hopf algebra of representations of the symmetric groups, the Hopf algebras of the nonsymmetric and quasisymmetric functions, and the Hopf algebra of permutations.

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Genre : Mathematics
Author : Michiel Hazewinkel
Publisher : American Mathematical Soc.
Release : 2010
File : 425 Pages
ISBN-13 : 9780821852620