Invariants of Unimodular Quadratic Polynomial Poisson Algebras of Dimension 3

2023/02/27 by Chengyuan Ma, Ma, Chengyuan
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2302.13588

openalex publication_date 2023/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let P = \Bbbk[x1,x2,x3] be a unimodular quadratic Poisson algebra and let G be a finite subgroup of the graded Poisson automorphism group of P. In this paper, we prove a variant of the Shephard-Todd-Chevalley theorem for P and variants the Shephard-Todd-Chevalley theorem and the Watanabe theorem for its Poisson enveloping algebra U(P) under the induced group \widetildeG.

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