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

Su, Hongbing

doi:10.1090/S0002-9947-96-01757-6

K-theoretic classification for certain inductive limit $Z_2$ actions on real rank zero $C^*$-algebras
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Trans. Amer. Math. Soc. 348 (1996), 4199-4230 Request permission

Abstract:

In this paper a K-theoretic classification is given of the C$^*$-algebra dynamical systems $(A, \alpha , Z_2)= \lim \limits _\to (A_n, {\alpha }_n, Z_2)$ where $A$ is of real rank zero, each $A_n$ is a finite direct sum of matrix algebras over finite connected graphs, and each $\alpha _n$ is induced by an action on each component of the spectrum of $A_n$. 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.

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