Trace-scaling automorphisms of certain stable AF algebras
D.E. Evans, A. Kishimoto
TL;DR
This paper proves that trace-scaling automorphisms of certain stable AF algebras are outer conjugate when they share the same scaling factor, extending known results from type II_infty factors and UHF algebras.
Contribution
It establishes a new conjugacy classification for trace-scaling automorphisms of stable AF algebras with totally ordered dimension groups.
Findings
Automorphisms with the same scaling factor are outer conjugate.
Extension of Connes' result from type II_infty factors.
Generalization of previous UHF algebra results.
Abstract
Trace scaling automorphisms of stable AF algebras with dimension group totally ordered are outer conjugate if the scaling factors are the same (not equal to one). This is an adaptation of a similar result for the AFD type II_infty factor by Connes and extends the previous result for stable UHF algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Logic