Free Gelfand-Dorfman-Novikov superalgebras and a Poincaré-Birkhoff-Witt type theorem

Zerui Zhang; Yuqun Chen; Leonid A. Bokut

doi:10.1142/S0218196719500115

Free Gelfand-Dorfman-Novikov superalgebras and a Poincaré-Birkhoff-Witt type theorem

Zerui Zhang, Yuqun Chen, Leonid A. Bokut

Кафедра дискретной математики и информатики ММФ и СУНЦ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

2 Цитирования (Scopus)

Аннотация

We construct linear bases of free Gelfand-Dorfman-Novikov (GDN) superalgebras. As applications, we prove a Poincare-Birkhoff-Witt (PBW) type theorem, that is, every GDN superalgebra can be embedded into its universal enveloping associative differential supercommuative algebra. An Engel theorem is given.

Язык оригинала	английский
Страницы (с-по)	481-505
Число страниц	25
Журнал	International Journal of Algebra and Computation
Том	29
Номер выпуска	3
DOI	https://doi.org/10.1142/S0218196719500115
Состояние	Опубликовано - 1 мая 2019

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10.1142/S0218196719500115

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abstract = "We construct linear bases of free Gelfand-Dorfman-Novikov (GDN) superalgebras. As applications, we prove a Poincare-Birkhoff-Witt (PBW) type theorem, that is, every GDN superalgebra can be embedded into its universal enveloping associative differential supercommuative algebra. An Engel theorem is given.",

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Free Gelfand-Dorfman-Novikov superalgebras and a Poincaré-Birkhoff-Witt type theorem. / Zhang, Zerui; Chen, Yuqun; Bokut, Leonid A.

В: International Journal of Algebra and Computation, Том 29, № 3, 01.05.2019, стр. 481-505.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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AU - Zhang, Zerui

AU - Chen, Yuqun

AU - Bokut, Leonid A.

PY - 2019/5/1

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N2 - We construct linear bases of free Gelfand-Dorfman-Novikov (GDN) superalgebras. As applications, we prove a Poincare-Birkhoff-Witt (PBW) type theorem, that is, every GDN superalgebra can be embedded into its universal enveloping associative differential supercommuative algebra. An Engel theorem is given.

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KW - GDN superalgebra

KW - nilpotency

KW - Poincaré-Birkhoff-Witt theorem

KW - ALGEBRAS

KW - Poincare-Birkhoff-Witt theorem

KW - CALCULUS

KW - HYDRODYNAMIC TYPE

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