K-theoretic classification for certain inductive limit 𝑍₂ actions on real rank zero 𝐶*-algebras

Abstract

In this paper a K-theoretic classification is given of the C ∗ ^* -algebra dynamical systems ( A , α , Z 2 ) = lim → ( A n , α n , Z 2 ) (A, \alpha , Z_2)= \lim \limits _\to (A_n, {\alpha }_n, Z_2) where A A is of real rank zero, each A n A_n is a finite direct sum of matrix algebras over finite connected graphs, and each α n \alpha _n is induced by an action on each component of the spectrum of A n A_n . Corresponding to the trivial actions is the K-theoretic classification for real rank zero C ∗ ^* -algebras that can be expressed as finite direct sums of matrix algebras over finite graphs obtained in Mem. Amer. Math. Soc. no. 547, vol. 114.