G-CENTRAL SUBALGEBRAS, AND EXTENSIONS OF KMS STATES

Let (A, G, α) be a G-central C*-dynamical system, and B be a separable, seminuclear, G-invariant, C*-subalgebra of B. Then (B, G, α | B) is G-central. If (B, R,τ) is any one-parameter C*-dynamical system, φ is a KMS state of B, and A is a C*-algebra containing B, then φ has a state extenstion ψ satisfying ψ(τi(b) a) = ψ(ab) for all a in A and all analytic b in B if and only if there is a contraction Q: A → πφ(B)″ such that Q | B = πφ. © 1986