Extension of K.M.S. states with respect to some locally compact groups (Q1070178)

Given a state \(\omega\) on the \(C^*\)-system \(\{{\mathcal A},{\mathbb{R}}\times G,\alpha\}\) which is K.M.S. with respect to time on the sub-algebra of \({\mathcal A}\) of fixed points under the action of some locally compact group G, we study its K.M.S.-extension to the whole algebra. In this work, we study more precisely the cases where G is a class of locally compact Abelian groups (such that \(\{{\mathcal A},G,\alpha | G\}\) is almost periodic) or a product of these groups with a compact group.