Automorphisms of dimension groups and the construction of AF algebras

Chao-Liang Shen

Type: Article

Publication Date: 1981-12-01

Citations: 26

DOI: https://doi.org/10.2140/pjm.1981.97.461

Abstract

Recent results of Edward G. Effros and the author show that if a dimension group is simple, totally ordered and with underlying group Z n , then we can construct explicitly an AF C*-algebra with the given group as its K o 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 (Z 3 , P a , a ,β)) being stationary is that both a 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.

Locations

Pacific Journal of Mathematics - View - PDF
Project Euclid (Cornell University) - View - PDF

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