Laurent Cantier (Universitat Autònoma de Barcelona)
The Cu$_1$-semigroup as an invariant for K$_1$-obstruction cases
Abstract: The aim of this talk is to explicitly shows that the unitary Cuntz semigroup, defined using the Cuntz semigroup and the K$_1$ group, strictly contains more information than the latter invariants alone. To that end, we construct two C*-algebras, distinguished by their unitary Cuntz semigroup, whose K-Theory and Cu-semigroup are isomorphic. Both A and B, constructed as inductive limits of NCCW 1-algebras, are non-simple unital separable C∗-algebras of stable rank one with K$_1$-obstructions. This shows that a likewise invariant is necessary in order to extend classification results of C*-algebras by means of Cuntz semigroup to the non trivial K$_1$ group case.