Cartan subalgebras and the UCT problem
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 satisfies the UCT if there is some automorphism of with the property that is regular, where denotes the canonical masa of . We prove that this condition is automatic if is not a masa or is inner conjugate to . Finally, we relate the UCT problem for separable, nuclear, -absorbing C*-algebras to Cartan subalgebras and order two automorphisms of .
Keywords
Cite
@article{arxiv.1511.02697,
title = {Cartan subalgebras and the UCT problem},
author = {Selçuk Barlak and Xin Li},
journal= {arXiv preprint arXiv:1511.02697},
year = {2017}
}
Comments
v3: 18 pages; minor modifcations, updated reference list, one new reference added. To appear in Adv. Math. v2: 18 pages; minor modifications mostly in Abstract, Introduction and Section 3. More significant changes in Section 4. Main results are unchanged. v1: 17 pages