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On free Gelfand–Dorfman–Novikov–Poisson algebras and a PBW theorem. / Bokut, L. A.; Chen, Yuqun; Zhang, Zerui.

In: Journal of Algebra, Vol. 500, 15.04.2018, p. 153-170.

Research output: Contribution to journal › Article › peer-review

Harvard

Bokut, LA, Chen, Y & Zhang, Z 2018, 'On free Gelfand–Dorfman–Novikov–Poisson algebras and a PBW theorem', Journal of Algebra, vol. 500, pp. 153-170. https://doi.org/10.1016/j.jalgebra.2016.12.006

APA

Bokut, L. A., Chen, Y., & Zhang, Z. (2018). On free Gelfand–Dorfman–Novikov–Poisson algebras and a PBW theorem. Journal of Algebra, 500, 153-170. https://doi.org/10.1016/j.jalgebra.2016.12.006

Vancouver

Bokut LA, Chen Y, Zhang Z. On free Gelfand–Dorfman–Novikov–Poisson algebras and a PBW theorem. Journal of Algebra. 2018 Apr 15;500:153-170. doi: 10.1016/j.jalgebra.2016.12.006

Author

Bokut, L. A. ; Chen, Yuqun ; Zhang, Zerui. / On free Gelfand–Dorfman–Novikov–Poisson algebras and a PBW theorem. In: Journal of Algebra. 2018 ; Vol. 500. pp. 153-170.

BibTeX

@article{64a4c82ab8aa4338b802324455f0b4c9,
title = "On free Gelfand–Dorfman–Novikov–Poisson algebras and a PBW theorem",
abstract = "In 1997, X. Xu [18,19] invented a concept of Novikov–Poisson algebras (we call them Gelfand–Dorfman–Novikov–Poisson (GDN–Poisson) algebras). We construct a linear basis of a free GDN–Poisson algebra. We define a notion of a special GDN–Poisson admissible algebra, based on X. Xu's definition and an S.I. Gelfand's observation (see [9]). It is a differential algebra with two commutative associative products and some extra identities. We prove that any GDN–Poisson algebra is embeddable into its universal enveloping special GDN–Poisson admissible algebra. Also we prove that any GDN–Poisson algebra with the identity x∘(y⋅z)=(x∘y)⋅z+(x∘z)⋅y is isomorphic to a commutative associative differential algebra.",
keywords = "GDN–Poisson algebra, Poincar{\'e}–Birkhoff–Witt theorem, Special GDN–Poisson admissible algebra, DERIVATION, BRACKETS, GDN-Poisson algebra, CHARACTERISTIC-0, algebra, NONASSOCIATIVE-ALGEBRAS, Special GDN-Poisson admissible, LIE-ALGEBRAS, Poincare-Birkhoff-Witt theorem, MODULES, HAMILTONIAN OPERATORS, SUPERALGEBRAS, HYDRODYNAMIC TYPE",
author = "Bokut, {L. A.} and Yuqun Chen and Zerui Zhang",
note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",
year = "2018",
month = apr,
day = "15",
doi = "10.1016/j.jalgebra.2016.12.006",
language = "English",
volume = "500",
pages = "153--170",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - On free Gelfand–Dorfman–Novikov–Poisson algebras and a PBW theorem

AU - Bokut, L. A.

AU - Chen, Yuqun

AU - Zhang, Zerui

N1 - Publisher Copyright: © 2016 Elsevier Inc.

PY - 2018/4/15

Y1 - 2018/4/15

N2 - In 1997, X. Xu [18,19] invented a concept of Novikov–Poisson algebras (we call them Gelfand–Dorfman–Novikov–Poisson (GDN–Poisson) algebras). We construct a linear basis of a free GDN–Poisson algebra. We define a notion of a special GDN–Poisson admissible algebra, based on X. Xu's definition and an S.I. Gelfand's observation (see [9]). It is a differential algebra with two commutative associative products and some extra identities. We prove that any GDN–Poisson algebra is embeddable into its universal enveloping special GDN–Poisson admissible algebra. Also we prove that any GDN–Poisson algebra with the identity x∘(y⋅z)=(x∘y)⋅z+(x∘z)⋅y is isomorphic to a commutative associative differential algebra.

AB - In 1997, X. Xu [18,19] invented a concept of Novikov–Poisson algebras (we call them Gelfand–Dorfman–Novikov–Poisson (GDN–Poisson) algebras). We construct a linear basis of a free GDN–Poisson algebra. We define a notion of a special GDN–Poisson admissible algebra, based on X. Xu's definition and an S.I. Gelfand's observation (see [9]). It is a differential algebra with two commutative associative products and some extra identities. We prove that any GDN–Poisson algebra is embeddable into its universal enveloping special GDN–Poisson admissible algebra. Also we prove that any GDN–Poisson algebra with the identity x∘(y⋅z)=(x∘y)⋅z+(x∘z)⋅y is isomorphic to a commutative associative differential algebra.

KW - GDN–Poisson algebra

KW - Poincaré–Birkhoff–Witt theorem

KW - Special GDN–Poisson admissible algebra

KW - DERIVATION

KW - BRACKETS

KW - GDN-Poisson algebra

KW - CHARACTERISTIC-0

KW - algebra

KW - NONASSOCIATIVE-ALGEBRAS

KW - Special GDN-Poisson admissible

KW - LIE-ALGEBRAS

KW - Poincare-Birkhoff-Witt theorem

KW - MODULES

KW - HAMILTONIAN OPERATORS

KW - SUPERALGEBRAS

KW - HYDRODYNAMIC TYPE

UR - http://www.scopus.com/inward/record.url?scp=85007568873&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2016.12.006

DO - 10.1016/j.jalgebra.2016.12.006

M3 - Article

AN - SCOPUS:85007568873

VL - 500

SP - 153

EP - 170

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 12232453