Minimal Bratteli diagrams and dimension groups of AF C*-algebras

2003/10/22 by Ryan J. Zerr, Zerr, Ryan J.
Mathematics · #46L40 #46L80 #47L40 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L40 #msc:46L80 #msc:47L40

paper · pdf · doi:10.48550/arxiv.math/0310360

arxiv created 2003/10/22 · arxiv updated 2009/12/01

Abstract

A method is described which identifies a wide variety of AF algebra dimension groups with groups of continuous functions. Since the continuous functions in these groups have domains which correspond to the set of all infinite paths in what will be called minimal Bratteli diagrams, it becomes possible, in some cases, to analyze the dimension group's order preserving automorphisms by utilizing the topological structure of the associated minimal Bratteli diagram.

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