Let be the AF algebra whose scaled ordered group is , where is the scaled ordered group of a unital simple AF algebra , and is a countable torsion-free Abelian group. Let be an order 2 scaled ordered automorphism of , defined by , where . We show that there is an order automorphism of such that . This gives a partial answer to a lifting question posed by Blackadar. Incidentally, the lift we construct has the tracial Rokhlin property. Consequently, the crossed product is a unital simple AH algebra with no dimension growth.
"On a lifting question of Blackadar." Ann. Funct. Anal. 9 (4) 485 - 499, November 2018. https://doi.org/10.1215/20088752-2017-0063