Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778548 | Advances in Mathematics | 2017 | 22 Pages |
Abstract
We show that a separable, nuclear C*-algebra satisfies the UCT if it has a Cartan subalgebra. Furthermore, we prove that the UCT is closed under crossed products by group actions which respect Cartan subalgebras. This observation allows us to deduce, among other things, that a crossed product O2âαZp satisfies the UCT if there is some automorphism γ of O2 with the property that γ(D2)âO2âαZp is regular, where D2 denotes the canonical masa of O2. We prove that this condition is automatic if γ(D2)âO2âαZp is not a masa or α(γ(D2)) is inner conjugate to γ(D2). Finally, we relate the UCT problem for separable, nuclear, M2â-absorbing C*-algebras to Cartan subalgebras and order two automorphisms of O2.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Selçuk Barlak, Xin Li,