Let be a unital simple -algebra of real rank zero. Given an order two automorphism , we show that there is an order two automorphism : such that , and the action of generated by has the tracial Rokhlin property. Consequently, is a simple unital AH-algebra with no dimension growth, and with tracial rank zero. Thus our main result can be considered as the -action analogue of the Lin-Osaka theorem. As a consequence, a positive answer to a lifting problem of Blackadar is also given for certain split case.
Cite this article
Yuanhang Zhang, Symmetries of simple -algebras. J. Noncommut. Geom. 17 (2023), no. 2, pp. 439–468DOI 10.4171/JNCG/492