G-central subalgebras, and extensions of KMS states (Q1072068)

Let (A,G,\(\alpha)\) be a G-central \(C^*\)-dynamical system, and B be a separable, seminuclear, G-invariant \(C^*\)-subalgebra of A. Then (B,G,\(\alpha\) \(| B)\) is G-central. If (B,\({\mathbb{R}},\tau)\) is any one- parameter \(C^*\)-dynamical system, \(\phi\) is a KMS state of B, and A is a \(C^*\)-algebra containing B, then \(\phi\) has a state extension \(\psi\) satisfying \(\psi (\tau_ i(b)a)=\psi (ab)\) for all a in A and all analytic b in B if and only if there is a contraction \(Q: A\to \pi_{\phi}(B)''\) such that \(Q| B=\pi_{\phi}\). These results are obtained from covariant versions of the study of extensions of factorial states by \textit{R. J. Archbold} and the author [J. Funct. Anal. 63, 86-100 (1985; Zbl 0576.46044)].