A note on extending Hopf actions to rings of quotients of module algebras. (Q2488601)

Let \(k\) be a commutative ring, \(H\) a Hopf \(k\)-algebra, \(A\) an \(H\)-module algebra and \(A\#H\) the smash product of \(A\) and \(H\). The author investigates sufficient conditions to extend the \(H\)-action on \(A\) to a localization of \(A\) (in particular to \(Q_{\mathcal F}(A)\), the ring of quotients with respect to the Gabriel topology \(\mathcal F:=\mathcal F_H\) which has a basis of \(H\)-stable \(\mathcal F\)-dense left ideals). For particular cases, localizations of \(A\) to which such an extension is possible are characterized.