Relative Dixmier property for Poisson algebras

Abstract: Dixmier property concerns the bijectivity of endomorphisms for algebras. We introduce a relative Dixmier property, which is a generalization of the Dixmier property. This new concept has applications in proving that several classes of Poisson algebras possess the Dixmier property, as well as in other topics such as the cancellation problem and the non-existence of Hopf coactions.