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arXiv · 1903.02238

Gelfand--Dorfman algebras, derived identities, and the Manin product of operads

P. S. Kolesnikov·B. Sartayev·A. Orazgaliev
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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 $a\succ b = d(a)b$ and $a\prec b = ad(b)$ on a (non-associative) differential algebra with a derivation~$d$.

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P. S. Kolesnikov, B. Sartayev, A. Orazgaliev. 2019-03-06. Gelfand--Dorfman algebras, derived identities, and the Manin product of operads. https://doi.org/10.1016/j.jalgebra.2019.07.034

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