Coxeter Graphs and Towers of Algebras

Coxeter Graphs and Towers of Algebras
Author: Frederick M. Goodman
Publisher: Springer Science & Business Media
Total Pages: 297
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461396417

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A recent paper on subfactors of von Neumann factors has stimulated much research in von Neumann algebras. It was discovered soon after the appearance of this paper that certain algebras which are used there for the analysis of subfactors could also be used to define a new polynomial invariant for links. Recent efforts to understand the fundamental nature of the new link invariants has led to connections with invariant theory, statistical mechanics and quantum theory. In turn, the link invariants, the notion of a quantum group, and the quantum Yang-Baxter equation have had a great impact on the study of subfactors. Our subject is certain algebraic and von Neumann algebraic topics closely related to the original paper. However, in order to promote, in a modest way, the contact between diverse fields of mathematics, we have tried to make this work accessible to the broadest audience. Consequently, this book contains much elementary expository material.

Operator Algebras and Applications

Operator Algebras and Applications
Author: David E. Evans
Publisher: Cambridge University Press
Total Pages: 253
Release: 1989
Genre: Mathematical physics
ISBN: 0521368448

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These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.

Conformal Field Theory

Conformal Field Theory
Author: Philippe Francesco
Publisher: Springer Science & Business Media
Total Pages: 908
Release: 2012-12-06
Genre: Science
ISBN: 1461222567

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Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Generalized Symmetries In Physics - Proceedings Of The International Symposium On Mathematical Physics

Generalized Symmetries In Physics - Proceedings Of The International Symposium On Mathematical Physics
Author: Heinz-dietrich Doebner
Publisher: World Scientific
Total Pages: 446
Release: 1994-07-05
Genre:
ISBN: 9814550884

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This volume contains material submitted to a symposium on mathematical physics in July 1993 at the Technical University of Clausthal. It focuses on mathematical and physical notions of symmetries, especially on generalized and quantum symmetries (quantum groups and algebras) with applications to integrable systems, quasi-exact solvability, quantization methods and nonlinear problems. The workshop is a continuation of the series of meetings and workshops on mathematical physics in Clausthal which brings together mathematicians, theoretical and mathematical physicists working in the different parts of generalized symmetries. Recent developments in the mathematical structure and physical applications of generalized symmetries are discussed.

Current Topics In Operator Algebras - Proceedings Of The Satellite Conference Of Icm - 90

Current Topics In Operator Algebras - Proceedings Of The Satellite Conference Of Icm - 90
Author: Y Nakagami
Publisher: World Scientific
Total Pages: 450
Release: 1991-04-29
Genre:
ISBN: 981455622X

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The topics covered in this proceedings include the C* — dynamical systems, the index theory of subfactors, the noncommutative differential geometry and the quantum groups. This volume presents an overview of the present status of the theory of operator algebras, as well as an outlook for its future development.

Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xxi International Conference

Differential Geometric Methods In Theoretical Physics - Proceedings Of The Xxi International Conference
Author: Chen Ning Yang
Publisher: World Scientific
Total Pages: 626
Release: 1993-07-31
Genre:
ISBN: 9814553778

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This volume contains intense studies on Quantum Groups, Knot Theory, Statistical Mechanics, Conformal Field Theory, Differential Geometry and Differential Equation Methods and so on. It has contributions by renowned experts and covers most of the recent developments in these fields.

Quantum and Non-Commutative Analysis

Quantum and Non-Commutative Analysis
Author: Huzihiro Araki
Publisher: Springer Science & Business Media
Total Pages: 452
Release: 2013-04-17
Genre: Science
ISBN: 9401728232

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In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Integrable Systems, Quantum Groups, and Quantum Field Theories

Integrable Systems, Quantum Groups, and Quantum Field Theories
Author: Alberto Ibort
Publisher: Springer Science & Business Media
Total Pages: 508
Release: 2012-12-06
Genre: Science
ISBN: 9401119805

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In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.