On the special identities of Gelfand--Dorfman algebras

Abstract

In this paper, we prove that the class of all special Gelfand--Dorfman algebras (GD-algebras) is closed with respect to homomorphisms and thus forms a variety. We also prove that every 2-dimensional GD-algebra is special. For the latter, we give a technical method to find all special identities of GD-algebras and compute the degree 6 component of the Gröbner basis for the shuffle operad constructed on the symmetric operad governing the class of GD-algebras.

Cited by in corpus (6)

• The algebraic and geometric classification of transposed Poisson algebras
• Transposed Poisson structures
• Noncommutative Novikov algebras
• Some generalizations of the variety of transposed Poisson algebras
• On the free metabelian Novikov and metabelian Lie-admissible algebras
• Differential envelopes of Novikov conformal algebras