Jones Index Theory for C*-Algebras
The notion of index [M : N] was introduced by Jones  as an invariant for subfactors N of a factor M of type II1. Subsequently Kosaki  defined an index E for a conditional expectation E of an arbitrary factor M onto a subfactor N using the spatial theory of Connes  and the theory of operator-valued weights of Haagerup . We shall define an index E for a conditional expectation E on a C*-algebra. This index theory for C*-algebras is a mixture of the index theory by Jones and the theory of Morita equivalence by Rieffel , . We establish the link between transfer in K -theory and a multiplication by Index E.
KeywordsConditional Expectation Operator Algebra Index Theory Basic Construction Irrational Rotation
Unable to display preview. Download preview PDF.
- J. Bion-Nadal, Von Neumann subalgebras of type II1 factors, correspondences and property T, preprint.Google Scholar
- M. Choda, Full II1-factors with non-integer index, preprint.Google Scholar
- F.M. Goodman, P. de la Harpe and V. Jones, Coxeter-Dynkin diagrams and towers of algebras, MSRI Publication 14, Springer-Verlag, Berlin (1989).Google Scholar
- T. Hamachi and H. Kosaki, Inclusion of type III factors constructed from ergodic flows, preprint.Google Scholar
- V. Jones, Braid Groups, Hecke Algebras and Type II1 Factors in Geometric Methods in Operator Algebras, Pitman Research Notes in Mathematics Series 123, (1986), 242–273.Google Scholar
- M.A. Rieffel, Morita equivalence for operator algebras, in Proc. Symposium Pure Math. 38, Part 1, 285–298.Google Scholar
- M.A. Rieffel, Applications of strong Morita equivalence to transformation group C*-algebras, in Proc. Symposium Pure Math. 38, Part 1, 299–310.Google Scholar
- S. Sakai, C*-Algebras and W*-Algebras, Ergebnisse der Math. vol. 60 (1971), Berlin-Heidelberg-New York.Google Scholar
- H. Wenzl, Representations of Hecke algebras and subfactors, Thesis, Univ. of Pennsylvania, 1985.Google Scholar
- H. Yoshida, On crossed products and relative entropy, preprintGoogle Scholar