Quantum Symmetries on Operator Algebras by David E. EvansQuantum Symmetries on Operator Algebras by David E. Evans

Quantum Symmetries on Operator Algebras

byDavid E. Evans, Yasuyuki Kawahigashi

Hardcover | June 1, 1998

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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.
(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, ...
Title:Quantum Symmetries on Operator AlgebrasFormat: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

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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