Operator algebras seminar
Jens Kaad (University of southern Denmark)
For a C*-correspondence from a C*-algebra to itself one may associate a C*-algebra referred to as the Cuntz-Pimsner algebra of the C*-correspondence. Special cases are the Cuntz-Krieger algebras and crossed products by the integers. Furthermore, the K-theory of Cuntz-Pimsner algebras can often be computed by means of a six term exact sequence which generalizes the K-theoretic Gysin-sequence of a complex hermitian line bundle.
A more general construction of C*-algebras associated to module theoretic data comes from subproduct systems over the monoid of non-negative integers. But so far in this context there are no general tools available for computing the K-groups of such a Cuntz-Pimsner algebra.
In this talk we investigate a class of C*-algebras constructed from a finite dimensional representation of SU(2) via an associated subproduct system. We indicate a procedure for computing the K-theory of this kind of Cuntz-Pimsner algebra by means of a six term exact sequence sharing the characteristic properties of the K-theoretic Gysin-sequence of a complex hermitian vector bundle of rank 2.
The talk is based on work in progress with Francesca Arici.