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arXiv · 2105.13815

On the special identities of Gelfand--Dorfman algebras

P. S. Kolesnikov·B. K. Sartayev
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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 Gr\"obner basis for the shuffle operad constructed on the symmetric operad governing the class of GD-algebras.

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P. S. Kolesnikov, B. K. Sartayev. 2021-05-28. On the special identities of Gelfand--Dorfman algebras. https://doi.org/10.1080/10586458.2022.2041134

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