Divisibility properties for C*-algebras

Abstract

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 $(A_n)$ of simple unital infinite dimensional C*-algebras such that the product ${\prod }_{n=1}^{\infty }{A}_n$ has a character.

Cited by in corpus (4)

• Tensor products and regularity properties of Cuntz semigroups
• Nuclear dimension and Z-stability of non-simple C*-algebras
• Nowhere scattered multiplier algebras
• Some Permanence properties for crossed products by compact group actions with the tracial Rokhlin property