Quantum Symmetries on Operator Algebras

(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

• 1. Operator theory basics ; 2. C*-algebra basics ; 3. K-theory ; 4. Positivity and semigroups ; 5. von Neumann algebra basics ; 6. The Fermion algebra ; 7. The Ising model ; 8. Conformal field theory ; 9. Subfactors and bimodules ; 10. Axiomatization of paragroups ; 11. String algebras and flat connections ; 12. Topological quantum field theory (TQFT) and paragroups ; 13. Rational conformal field theory (RCFT) and paragroups ; 14. Commuting squares of II1 factors ; 15. Automorphisms of subfactors and central sequences ; Bibliography ; Index

'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