Classification of certain inductive limit actions of compact groups on AF algebras

摘要

Let $A=underrightarrow{lim}{A_n}$ be an AF algebra, $G$ be a compact group.We consider inductive limit actions of the form$lpha=underrightarrow{lim}{lpha_n}$, where $lpha_ncolonGcurvearrowright A_n$ is an action on the finite dimensional C*-algebra $A_n$which fixes each matrix summand. If each $lpha_n$ is inner, such actions areclassified by equivariant K-theory by Handelman and Rossmann. However, if theactions $lpha_n$ are not inner, we show that such actions are notclassifiable by equivariant K-theory. We give a complete classification of suchactions using twisted equivariant K-theory.