Word problem for finitely presented metabelian Poisson algebras

2019/07/11 by Zerui Zhang, Zhang, Zerui, Yuqun Chen +3
Computer Science · Mathematics · #13P10 #16S15 #17B63 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1907.05953

openalex publication_date 2019/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first construct a linear basis for a free metabelian Poisson algebra generated by an arbitrary well-ordered set. It turns out that such a linear basis depends on the characteristic of the underlying field. Then we elaborate the method of Gröbner--Shirshov bases for metabelian Poisson algebras. Finally, we show that the word problem for finitely presented metabelian Poisson algebras are solvable.

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