Strict comparison for C*-algebras arising from almost finite groupoids

In this paper we show that for an almost finite minimal ample groupoid G, its reduced C∗-algebra C∗r(G) has real rank zero and strict comparison even though C∗r(G) may not be nuclear in general. Moreover, if we further assume G being also second countable and non-elementary, then its Cuntz semigroup Cu(C∗r(G)) is almost divisible and Cu(C∗r(G)) and Cu(C∗r(G)⊗Z) are canonically order-isomorphic, where Z denotes the Jiang-Su algebra

Isomorphism and Morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of SL2(Z)

Abstract not available

A note on crossed products of rotation algebras

We compute the K -theory of crossed products of rotation algebras A θ , for any real angle θ , by matrices in S L ( 2 , Z ) with infinite order. Using techniques of continuous fields, we show that the canonical inclusion of A θ into the crossed products is injective at the level of K 0 -groups. We then give an explicit set of generators for the K 0 -groups and compute the tracial ranges concretely

The Cuntz–Toeplitz algebras have nuclear dimension one

We prove that unital extensions of Kirchberg algebras by separable stable AF algebras have nuclear dimension one. The title follows