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Non-stationarity of isomorphism between AF algebras defined by stationary Bratteli diagrams

Published online by Cambridge University Press:  01 December 2000

OLA BRATTELI ,
PALLE E. T. JØRGENSEN ,
KI HANG KIM  and
FRED ROUSH
OLA BRATTELI
Affiliation:
Mathematics Institute, University of Oslo, PB 1053 Blindern, N-0316 Oslo, Norway (e-mail: bratteli@math.uio.no)
PALLE E. T. JØRGENSEN
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA (e-mail: jorgen@math.uiowa.edu)
KI HANG KIM
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, AL 36101-0271, USA (e-mail: {kkim, froush}@asu.alasu.edu)
FRED ROUSH
Affiliation:
Mathematics Research Group, Alabama State University, Montgomery, AL 36101-0271, USA (e-mail: {kkim, froush}@asu.alasu.edu)
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Abstract

We first study situations where the stable AF algebras defined by two square primitive non-singular incidence matrices with non-negative integer matrix elements are isomorphic, even though no powers of the associated automorphisms of thecorresponding dimension groups are isomorphic. More generally we consider necessary and sufficient conditions for two such matrices to determine isomorphic dimension groups.We give several examples.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 6 , December 2000 , pp. 1639 - 1656
Copyright
© 2000 Cambridge University Press

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