Remarks on Villadsen algebras (Q6581820)

This paper is about Villadsen algebras of the first type and the question of how to classify them. In general, these Villadsen algebras do not absorb the Jiang-Su algebra tensorially and hence cannot be covered by the current classification theorem. Roughly speaking, the authors' main results tell us that for special classes of Villadsen algebras, the Elliott invariant together with the radius of comparison is a complete invariant. The radius of comparison is a notion introduced by Andrew Toms and has been used to distinguish C*-algebras with the same Elliott invariant, eventually leading to Toms' examples which cannot be classified by the Elliott invariant.