Titles and Abstracts for the Algebra Extravaganza

Title: The Dixmier-Moeglin equivalence for D-groups Abstract: The Dixmier-Moeglin equivalence is a characterization of the primitive ideals of an algebra that holds for many classes of rings, including affine PI rings, enveloping algebras of finite-dimensional Lie algebras, and many quantum algebras. For rings satisfying this equivalence, it says that the primitive ideals are precisely those prime ideals that are locally closed in the Zariski topology and are also those prime ideals that are rational. We investigate a differential-algebraic/geometric analogue of this equivalence and show that it holds for a Dgroups, which we’ll define in the talk. We use this to show that the classical Dixmier-Moeglin equivalence holds for Hopf Ore extensions of commutative Hopf algebras. This is joint work with Omar Leon Sanchez and Rahim Moosa.