1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Department of Mathematics, University of Louisiana at Lafayette, USA3 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility behaviour. As a byproduct of our investigations, we show that there exists a sequence (An) of simple unital infinite dimensional C*-algebras such that the product ∏n=1∞ An has a character.
London Mathematical Society. Proceedings, 2013, Vol 106, Issue 6, p. 1330-1370