Translator Disclaimer
November 2018 On a lifting question of Blackadar
Yuanhang Zhang
Ann. Funct. Anal. 9(4): 485-499 (November 2018). DOI: 10.1215/20088752-2017-0063

Abstract

Let A be the AF algebra whose scaled ordered group K0(A) is (GH,(G+{0})H{(0,0)},g˜0), where (G,G+,g˜) is the scaled ordered group K0(B) of a unital simple AF algebra B, and H is a countable torsion-free Abelian group. Let σ be an order 2 scaled ordered automorphism of K0(A), defined by σ(g,h)=(g,h), where (g,h)GH. We show that there is an order 2 automorphism α of A such that α=σ. This gives a partial answer to a lifting question posed by Blackadar. Incidentally, the lift α we construct has the tracial Rokhlin property. Consequently, the crossed product C(Z2,A,α) is a unital simple AH algebra with no dimension growth.

Citation

Download Citation

Yuanhang Zhang. "On a lifting question of Blackadar." Ann. Funct. Anal. 9 (4) 485 - 499, November 2018. https://doi.org/10.1215/20088752-2017-0063

Information

Received: 3 October 2017; Accepted: 14 November 2017; Published: November 2018
First available in Project Euclid: 4 May 2018

zbMATH: 07002086
MathSciNet: MR3871909
Digital Object Identifier: 10.1215/20088752-2017-0063

Subjects:
Primary: 46L05
Secondary: 46L35

Rights: Copyright © 2018 Tusi Mathematical Research Group

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.9 • No. 4 • November 2018
Back to Top