On the Special Identities of Gelfand–Dorfman Algebras

P. S. Kolesnikov, B. K. Sartayev

2022

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DOI 10.1080/10586458.2022.2041134

Data confidence 70 medium

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Abstract

A Gelfand–Dorfman algebra (GD-algebra) is said to be special if it can be embedded into a differential Poisson algebra. In this paper, we prove that the class of all special GD-algebras is closed with respect to homomorphisms and thus forms a variety. We describe a technique for finding potentially all special identities of GD-algebras and derive two known special identities of degree 4 in this way. By computing the Gröbner basis for the corresponding shuffle operad, we show that these two identities imply all special ones up to degree 5.