Quantum Symmetries on Operator Algebras (Oxford Mathematical Monographs) by David E. Evans (PDF)

Description

In the last 20 years, the study of operator algebras has developed from a branch of functional analysis to a central field of mathematics with applications in both pure mathematics and mathematical physics. The theory was initiated by von Neumann and Murray as a tool for studying group representations and as a framework for quantum mechanics, and has since kept in touch with its roots in physics as a framework for quantum statistical mechanics and the formalism of algebraic quantum field theory. However, in 1981, the study of operator algebras took a new turn with the introduction by Vaughn Jones of subfactor theory, leading to remarkable connections with knot theory, 3-manifolds, quantum groups, and integrable systems in statistical mechanics and conformal field theory. This book, one of the first in the area, looks at these combinatorial-algebraic developments from the perspective of operator algebras. With minimal prerequisites from classical theory, it brings the reader tothe forefront of research.

User’s Reviews

Editorial Reviews: Review ‘This is a most remarkable book, and it certainly gives a hand to many mathematician, researchers as well as graduate students. On less than 850 pages, the author present vital information about 124 subjects in 15 chapters, in a manner accessible to any broadly trained analyst…..As a collection of broad and relevant information the book bears some similarity to the famous volumes of Dunford and Scwarz’ Zentralblatt Mathematik’This monumental book presents some of the most exciting developments of the past 15 years within operator algebra theory and its interaction with mathematical physics and algebraic topology…In the preface the authors state:this is aimed at graduate students and researchers in operator algebras, and statistical mechanics, algebraic, topolgical and conformal field theory and low dimensional topological invarieants. All ot these will find a rich source of study and references in this extensively annotated and documented volume, and not least a wide range of new perspectives on their own subject.’ Mathematical Reviews’ This monumental book presents some of the most exciting developments of the past 15 years within operator algebra theory and its interaction with mathematical physics and algebraic topology … a rich source of study and references in this extensively annotated and documented volume, and not least a wide range of new perspectives on their own subject’ MathsSciNet About the Author (until early 1998) Professor David E. Evans, Professor of Mathematics, Department of Mathematics, University of Wales, Swansea, Singleton Park, Swansea, SA2 8PP, WALES. Tel: +44 1792 295460; fax: +44 1792 295843; email: David.E.Evans@swansea.ac.uk (from early 1998) Mathematics Institute, University of Wales, Cardiff, Senghennydd Road, Cardiff CF2 4YH Tel: +44 1222 874827; fax: +44 1222 874199 Professor Yasuyuki Kawahigashi, Associate Professor, Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153, JAPAN. Tel: +81 3 5465 7024; fax: +81 3 5465 7012; email: yasuyuki@ms.u-tokyo.ac.jp

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Students and researchers can find here the material which lies at the foundation of the subject, and read about the latest and most exciting developments in this wonderful book.– Material which would otherwise be difficult to extract from the diverse journal literature in math and in physics. The bibliography and the index are both great as well. The treatment of the material in the book aims at students interested in operator algebras, mathematical physics, [especially statistical mechanics and conformal field theory], and low dimensional topology. The book starts with a very nice treatment of the basics in operator algebras, K-theory, and it then moves on to the applications: eg., the Ising model, subfactors and bimodels, the Jones index [for subfactors] and its applications, topological quantum field theory, and more.

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