Submission date: 7 November 2019

Abstract:

Recent work using the model theory of differentially closed fields to answer questions having to do with the Dixmier-Moeglin equivalence for (noncommutatve) finitely generated noetherian algebras, and for (commutative) finitely generated Poisson algebras, is here surveyed, with an emphasis on the model-theoretic and differential-algebraic-geometric antecedents.

Mathematics Subject Classification: 03C98, 12H05

Keywords and phrases: D-groups, D-varieties, differentially closed fields, Dixmier-Moeglin equivalence, Hopf algebra, internality, Jouanolou's theorem, Poisson algebra

Full text arXiv 1911.02959: pdf, ps.