Strongly Self-Absorbing C*-algebras which contain a nontrivial projection

TL;DR

This paper proves that strongly self-absorbing C*-algebras with a nontrivial projection have real rank zero and absorb the Jiang-Su algebra, providing new insights into their structure and classification.

Contribution

It establishes that such algebras are of real rank zero and absorb the Jiang-Su algebra, and explores conditions for automatic UCT and K-theoretical characterizations.

Findings

Strongly self-absorbing C*-algebras with a nontrivial projection have real rank zero.

These algebras absorb the Jiang-Su algebra.

Conditions for UCT and K-theoretical criteria for Kirchberg algebras are identified.

Abstract

It is shown that a strongly self-absorbing C*-algebra is of real rank zero and absorbs the Jiang-Su algebra if it contains a nontrivial projection. We also consider cases where the UCT is automatic for strongly self-absorbing C*-algebras, and K-theoretical ways of characterizing when Kirchberg algebras are strongly self-absorbing.