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

L. A. Bokut, Yuqun Chen, Zerui Zhang

Результат исследования: Научные публикации в периодических изданияхстатья

4 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)153-170
Число страниц18
ЖурналJournal of Algebra
Том500
DOI
СостояниеОпубликовано - 15 апр 2018

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