On the Special Identities of Gelfand–Dorfman Algebras
Kolesnikov P.S. Sartayev B.K.
2024Taylor and Francis Ltd.
Experimental Mathematics
2024#33Issue 1165 - 174 pp.
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.
Gelfand–Dorfman algebra , Gröbner basis , operad , Poisson algebra , special identity
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Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
Suleyman Demirel University, Kaskelen, Kazakhstan
Sobolev Institute of Mathematics
Suleyman Demirel University
10 лет помогаем публиковать статьи Международный издатель
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