Submission date: 1 December 2016

Abstract:

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.

Mathematics Subject Classification: 03C60, 12H05, 16T05, 16S36

Keywords and phrases: D-groups, model theory of differentially closed fields, Dixmier-Moeglin equivalence, Hopf Ore extensions.

Full text arXiv 1612.00069: pdf, ps.