The word problem for finitely presented metabelian Poisson algebras is solvable via a characteristic-dependent linear basis and Gröbner-Shirshov bases.
Hilbert, Ueber die Theorie der algebraischen Formen, Mathematische Annalen, 36(4) (1890) 473–534
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Word problem for finitely presented metabelian Poisson algebras
The word problem for finitely presented metabelian Poisson algebras is solvable via a characteristic-dependent linear basis and Gröbner-Shirshov bases.