On approximately inner automorphisms of certain crossed product 𝐶*-algebras

Dădărlat, Marius; Pasnicu, Cornel

doi:10.1090/S0002-9939-1990-1021897-4

On approximately inner automorphisms of certain crossed product $C^ *$-algebras
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by Marius Dădărlat and Cornel Pasnicu PDF

Proc. Amer. Math. Soc. 110 (1990), 383-385 Request permission

Abstract:

Let $G$ be a compact connected topological group having a dense subgroup isomorphic to $\mathbf {Z}$. Let $C(G) \stackrel {\rtimes }{\propto } \mathbf {Z}$ be the crossed product $C^*$-algebra of $C(G)$ with $\mathbf {Z}$, where $\mathbf {Z}$ acts on $G$ by rotations. Automorphisms of $C(G) \stackrel {\rtimes }{\propto } \mathbf {Z}$ leaving invariant the canonical copy of $C(G)$ are shown to be approximately inner iff they act trivially on $K_1(C(G) \stackrel {\rtimes }{\propto } \mathbf {Z})$.

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