Quantum Symmetries on Operator Algebras

Hardcover | June 1, 1998

byDavid E. Evans, Yasuyuki Kawahigashi

not yet rated|write a review
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 and connections with different areas in both pure mathematics (foliations, index theory, K-theory, cyclic homology, affine Kac--Moodyalgebras, quantum groups, low dimensional topology) and mathematical physics (integrable theories, statistical mechanics, conformal field theories and the string theories of elementary particles). The theory of operator algebras was initiated by von Neumann and Murray as a tool for studying grouprepresentations 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 theintroduction by Vaughan Jones of subfactor theory and remarkable connections were found with knot theory, 3-manifolds, quantum groups and integrable systems in statistical mechanics and conformal field theory. The purpose of this book, one of the first in the area, is to look at thesecombinatorial-algebraic developments from the perspective of operator algebras; to bring the reader to the frontline of research with the minimum of prerequisites from classical theory.

Pricing and Purchase Info

$460.80 online
$607.50 list price (save 24%)
Ships within 1-3 weeks
Ships free on orders over $25

From the Publisher

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 and connections with different areas in both pure mathematics (foliations, index theory, K-theory, cyclic homology, affine Kac--Moodyalgebras, quantum groups, low dimensional topolo...

(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,...

other books by David E. Evans

Crash Course Cardiovascular System
Crash Course Cardiovascular System

Kobo ebook|Apr 25 2012

$52.48

The Woodland Southeast
The Woodland Southeast

Kobo ebook|Sep 15 2009

$50.49 online$65.55list price(save 22%)
see all books by David E. Evans
Format:HardcoverDimensions:846 pages, 9.21 × 6.14 × 1.89 inPublished:June 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198511752

ISBN - 13:9780198511755

Look for similar items by category:

Customer Reviews of Quantum Symmetries on Operator Algebras

Reviews

Extra Content

Table of Contents

1. Operator theory basics2. C*-algebra basics3. K-theory4. Positivity and semigroups5. von Neumann algebra basics6. The Fermion algebra7. The Ising model8. Conformal field theory9. Subfactors and bimodules10. Axiomatization of paragroups11. String algebras and flat connections12. Topological quantum field theory (TQFT) and paragroups13. Rational conformal field theory (RCFT) and paragroups14. Commuting squares of II1 factors15. Automorphisms of subfactors and central sequencesBibliographyIndex

Editorial 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 notleast a wide range of new perspectives on their own subject' MathsSciNet