Vol. 97, No. 2, 1981

Recent Issues
Vol. 332: 1
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Automorphisms of dimension groups and the construction of AF algebras

Chao-Liang Shen

Vol. 97 (1981), No. 2, 461–469
Abstract

Recent results of Edward G. Effros and the author show that if a dimension group is simple, totally ordered and with underlying group Zn, then we can construct explicitly an AF C-algebra with the given group as its K0 by using the Jacobi-Perron algorithm. While the Jacobi-Perron algorithm breaks down for nontotally ordered groups, we study the construction problem via the consideration of automorphisms of the dimension group. We find the necessary and sufficient condition for a nontotally ordered simple dimension group (Z3,P(1,α,β)) being stationary is that both α and β lie in the same quadratic number field. We also provide an explicit method for constructing Bratteli diagrams (and hence corresponding AF C-algebras) for this type of groups.

Mathematical Subject Classification 2000
Primary: 46L05
Secondary: 06F20, 22A25
Milestones
Received: 10 March 1980
Published: 1 December 1981
Authors
Chao-Liang Shen