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

Zerui Zhang, Yuqun Chen, Leonid A. Bokut

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)481-505
Number of pages25
JournalInternational Journal of Algebra and Computation
Volume29
Issue number3
DOIs
Publication statusPublished - 1 May 2019

Keywords

  • GDN superalgebra
  • nilpotency
  • Poincaré-Birkhoff-Witt theorem
  • ALGEBRAS
  • Poincare-Birkhoff-Witt theorem
  • CALCULUS
  • HYDRODYNAMIC TYPE

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