#### Vol. 12, No. 2, 2018

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors' Addresses Editors' Interests Scientific Advantages Submission Guidelines Submission Form Editorial Login Author Index To Appear ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print)
$D$-groups and the Dixmier–Moeglin equivalence

### Jason Bell, Omar León Sánchez and Rahim Moosa

Vol. 12 (2018), No. 2, 343–378
##### 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 in the sense of Brown et al., “Connected Hopf algebras and iterated Ore extensions”, J. Pure Appl. Algebra 219:6 (2015).

##### Keywords
$D$-groups, model theory of differentially closed fields, Dixmier–Moeglin equivalence, Hopf Ore extensions
##### Mathematical Subject Classification 2010
Primary: 03C98
Secondary: 12H05, 16S36, 16T05