On the special identities of Gelfand--Dorfman algebras
arXiv:2105.13815 · doi:10.1080/10586458.2022.2041134
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.
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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