We establish Gröbner-Shirshov base 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.
- commutative differential algebra
- Gelfand-Dorfman-Novikov algebra
- Gröbner-Shirshov basis
- word problem
- HAMILTONIAN OPERATORS
- Grobner-Shirshov basis