46 research outputs found
C*-algebras of Hilbert module product systems
We consider a class of C*-algebras associated to one parameter continuous
tensor product systems of Hilbert modules, which can be viewed as continuous
counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of
quasihomomorphisms, we prove that those algebras are -contractible. One
special case is closely related to the Rieffel-Wiener-Hopf extension of a
crossed product by R considered by Rieffel and by Pimsner and Voiculescu, and
can be used to produce a new proof of Connes' analogue of the Thom isomorphism
and in particular of Bott periodicity. Another special case is closely related
to Arveson's spectral C*-algebras, and is used to settle Arveson's problem of
computing their K-theory, extending earlier results of Zacharias to cover the
general case.Comment: 11 pages (added an example and an appendix, corrected typos and
improved exposition