Symmetries of simple -algebras
Yuanhang Zhang
Jilin University, Changchun, China
![Symmetries of simple $A\mathbb{T}$-algebras cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jncg-volume-17-issue-2.png&w=3840&q=90)
Abstract
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. 439–468
DOI 10.4171/JNCG/492