Gr\"obner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras
Abstract
We establish Gr\"obner-Shirshov bases theory for Gelfand-Dorfman-Novikov algebras over a field of characteristic 0. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand-Dorfman-Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand-Dorfman-Novikov algebra which is not free.
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