Real rank zero for purely infinite corona algebras

Ping Wong Ng  (University of Louisiana at Lafayette)

10:00 am - 11:00 am, May 10h, 2016   Science Building A1510

Abstract:

Let $A$ be a nonunital simple separable $C^*$-algebra with strict comparison, almost divisibility, stable rank one, and quasicontinuous scale.Then the corona algebra $M(A)/A$ has real rank zero.
The above generalizes a number of results in the literature.
The proof techniques are based on the following (earlier) result:
Theorem: Let $A$ be a nonunital simple separable $C^*$-algebra with strict comparison, almost divisibility,and stable rank one.Then the following statements are equivalent:
(i.) $A$ has quasicontinuous scale.
(ii.) $M(A)$ has strict comparison.
(iii.) $M(A)/A$ is purely infinite.
(iv.) $M(A)/I_{min}$ is purely infinite.
(v.) $M(A)$ has finitely many ideals.
(vi.) $I_{min} = I_{fin}$.