D-groups and the Dixmier–Moeglin equivalence

A differential-algebraic geometric analogue of the Dixmier–Moeglin equivalence is articulated, and proven to hold for D-groups over the constants. The model theory of differentially closed fields of characteristic zero, in particular the notion of analysability in the constants, plays a central role. As an application it is shown that if R is a commutative affine Hopf algebra over a field of characteristic zero, and A is an Ore extension to which the Hopf algebra structure extends, then A satisfies the classical Dixmier–Moeglin equivalence. Along the way it is shown that all such A are Hopf Ore extensions in the sense of Brown et al., “Connected Hopf algebras and iterated Ore extensions”, J. Pure Appl. Algebra 219:6 (2015).