Mathematics – Operator Algebras
Scientific paper
2010-04-10
Mathematics
Operator Algebras
22 pages, the case of line bundles was added to the paper
Scientific paper
We prove that the Cuntz-Pimsner algebra O(E) of a vector bundle E over a compact metrizable space X is determined up to an isomorphism of C(X)-algebras by the ideal (1-[E])K(X) of the K-theory ring K(X). Moreover, if E and F are vector bundles of rank >1, then a unital embedding of C(X)-algebras of O(E) into O(F) exists if and only if 1-[E] is divisible by 1-[F] in the ring K(X). We introduce related, but more computable K-theory and cohomology invariants for O(E) and study their completeness. As an application we classify the unital separable continuous fields with fibers isomorphic to the Cuntz algebra O(m+1) over a finite connected CW complex X of dimension d< 2m+4 provided that the cohomology of X has no m-torsion.
No associations
LandOfFree
The C*-algebra of a vector bundle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The C*-algebra of a vector bundle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The C*-algebra of a vector bundle will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-600449