On free Gelfand-Dorfman-Novikov-Poisson algebras and a PBW theorem

DOI10.1016/J.JALGEBRA.2016.12.006zbMath1456.17001arXiv1604.06676OpenAlexW2473918016MaRDI QIDQ1702694

Zerui Zhang, Yuqun Chen, Leonid A. Bokut'

Publication date: 28 February 2018

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.06676

zbMATH Keywords

Poincaré-Birkhoff-Witt theoremGelfand-Dorfman-Novikov-Poisson algebraspecial Gelfand-Dorfman-Novikov-Poisson admissible algebra

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Poisson algebras (17B63) Nonassociative algebras satisfying other identities (17A30) Free nonassociative algebras (17A50)

Related Items (14)

Transposed BiHom-Poisson algebras ⋮ On the Lie-solvability of Novikov algebras ⋮ One-generated nilpotent Novikov algebras ⋮ Cohomology and deformation quantization of Poisson conformal algebras ⋮ Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras ⋮ Polynomial identities in Novikov algebras ⋮ On radicals of Novikov algebras ⋮ On the Special Identities of Gelfand–Dorfman Algebras ⋮ Invariant theory of free bicommutative algebras ⋮ Gröbner-Shirshov bases for free Gelfand-Dorfman-Novokov algebras and for right ideals of free right Leibniz algebras ⋮ Free Gelfand–Dorfman–Novikov superalgebras and a Poincaré–Birkhoff–Witt type theorem ⋮ Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Gelfand-Dorfman algebras, derived identities, and the Manin product of operads ⋮ On the solvability of graded Novikov algebras

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