Relative Dixmier property for Poisson algebras
Algebraic Geometry
2026-01-27 v1 Commutative Algebra
Rings and Algebras
Representation Theory
Abstract
Dixmier property concerns the bijectivity of endomorphisms for algebras. We introduce a relative Dixmier property, which is a generalization of the Dixmier property. This new concept has applications in proving that several classes of Poisson algebras possess the Dixmier property, as well as in other topics such as the cancellation problem and the non-existence of Hopf coactions.
Cite
@article{arxiv.2601.18249,
title = {Relative Dixmier property for Poisson algebras},
author = {Hongdi Huang and Zahra Nazemian and Xin Tang and Xingting Wang and Yanhua Wang and James J. Zhang},
journal= {arXiv preprint arXiv:2601.18249},
year = {2026}
}