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arXiv · 1904.05836

The Zariski cancellation problem for Poisson algebras

Jason Gaddis·Xingting Wang
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Abstract

We study the Zariski cancellation problem for Poisson algebras asking whether $A[t]\cong B[t]$ implies $A\cong B$ when $A$ and $B$ are Poisson algebras. We resolve this affirmatively in the cases when $A$ and $B$ are both connected graded Poisson algebras finitely generated in degree one without degree one Poisson central elements and when $A$ is a Poisson integral domain of Krull dimension two with nontrivial Poisson bracket. We further introduce Poisson analogues of the Makar-Limanov invariant and the discriminant to deal with the Zariski cancellation problem for other families of Poisson algebras.

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Jason Gaddis, Xingting Wang. 2019-04-11. The Zariski cancellation problem for Poisson algebras. https://doi.org/10.1112/jlms.12303

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