Aperiodic automorphisms of the Razak--Jacelon algebra

Abstract

We completely classify aperiodic automorphisms of the Razak--Jacelon algebra $\mathcal{W}$ up to outer conjugacy. As a technical ingredient, based on the works of Connes, Herman--Ocneanu, Kishimoto, and Sato, we introduce a notion of weak stability for automorphisms of simple separable monotracial C${}^{\ast }$-algebras. We also consider automorphisms of UHF algebras of infinite type and the Jiang--Su algebra. In particular, we classify aperiodic ``UHF-absorbing'' automorphisms of UHF algebras of infinite type up to outer conjugacy.

arXiv comment29 pages v3: minor revisions. v2: We have added the classification of aperiodic UHF-absorbing automorphisms of UHF algebras of infinite type (Theorem C)