Gr\"{o}bner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras
L.A. Bokut, Yuqun Chen, Zerui Zhang
TL;DR
This paper develops a Gr"{o}bner-Shirshov bases framework for Gelfand-Dorfman-Novikov algebras, providing a PBW theorem, an algorithm for the word problem, and a counterexample regarding free subalgebras.
Contribution
It introduces a Gr"{o}bner-Shirshov bases theory for Gelfand-Dorfman-Novikov algebras, including a PBW theorem and an algorithm for the word problem.
Findings
Established Gr"{o}bner-Shirshov bases theory for these algebras.
Provided a PBW type theorem in Shirshov form.
Developed an algorithm to solve the word problem for finite homogeneous relations.
Abstract
We establish Gr\"{o}bner-Shirshov bases theory for Gelfand-Dorfman-Novikov algebras over a field of characteristic . 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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