Abstract
Gelfand–Dorfman bialgebras (GD-algebras) are nonassociative systems with two bilinear operations satisfying a series of identities that express Hamiltonian property of an operator in the formal calculus of variations. The paper is devoted to the study of GD-algebras related with differential Poisson algebras. As a byproduct, we obtain a general description of identities that hold for operations a≻b=d(a)b and a≺b=ad(b) on a (non-associative) differential algebra with a derivation d.
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