Relative Dixmier property for Poisson algebras
Hongdi Huang, Zahra Nazemian, Xin Tang, Xingting Wang, Yanhua Wang, James J. Zhang
TL;DR
This paper introduces a relative Dixmier property for Poisson algebras, generalizing the classical property, and demonstrates its applications in algebraic structures and related mathematical problems.
Contribution
It defines a new relative Dixmier property and applies it to establish the Dixmier property in various Poisson algebras and related areas.
Findings
Several classes of Poisson algebras have the Dixmier property
Applications to the cancellation problem in algebra
Results on the non-existence of Hopf coactions
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Holomorphic and Operator Theory · Homotopy and Cohomology in Algebraic Topology