Every classifiable simple C*-algebra has a Cartan subalgebra
arXiv:1802.01190
summary
The paper constructs Cartan subalgebras in all classifiable stably finite C*-algebras and, together with existing results for UCT Kirchberg algebras, shows that every classifiable simple C*-algebra has a Cartan subalgebra.
Abstract
We construct Cartan subalgebras in all classifiable stably finite C*-algebras. Together with known constructions of Cartan subalgebras in all UCT Kirchberg algebras, this shows that every classifiable simple C*-algebra has a Cartan subalgebra.
final version, accepted for publication in Invent. Math.; title changed, results improved; 29 pages
Topics & keywords
#c*-algebras#cartan subalgebras#classification#stably finite#kirchberg algebrasCartan subalgebraclassifiable C*-algebraUCTKirchberg algebrastable finiteness