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Word problem for finitely presented metabelian Poisson algebras (1907.05953v1)
Published 11 Jul 2019 in math.RA
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 Gr\"{o}bner--Shirshov bases for metabelian Poisson algebras. Finally, we show that the word problem for finitely presented metabelian Poisson algebras are solvable.