Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras

Abstract

We establish Gröbner-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.

22 pages

References in corpus (1)

• Gröbner-Shirshov bases and their calculation

Cited by in corpus (7)

• Gelfand--Dorfman algebras, derived identities, and the Manin product of operads
• On the special identities of Gelfand--Dorfman algebras
• Endofunctors and Poincaré-Birkhoff-Witt theorems
• Noncommutative Novikov algebras
• The algebraic and geometric classification of $\delta$-Novikov algebras
• Differential envelopes of Novikov conformal algebras
• Derived operations satisfy standard identities