Submission date: 5 November 2021

Abstract:

Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a biderivation, namely a binary operation that is a derivation in each argument, is here begun, with an eye toward the geometry of the corresponding B-varieties. Foundational results about extending biderivations to localisations, algebraic extensions and transcendental extensions are established. Resolving a deficiency in Poisson algebraic geometry, a theory of base extension is achieved, and it is shown that dominant B-morphisms admit generic B-fibres. A bidifferential version of the Dixmier-Moeglin equivalence problem is articulated.

Mathematics Subject Classification: 12H05, 13N15, 16W25, 17B63

Keywords and phrases: biderivation, Poisson bracket, D-variety, Dixmier-Moeglin equivalence

Full text arXiv 2111.03475: pdf, ps.