Gröbner-Shirshov bases method for Gelfand-Dorfman-Novikov algebras

L. A. Bokut, Yuqun Chen, Zerui Zhang

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We establish Gröbner-Shirshov base theory for Gelfand-Dorfman-Novikov algebras over a field of characteristic 0. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand-Dorfman-Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand-Dorfman-Novikov algebra which is not free.

Original languageEnglish
Article number1750001
Number of pages22
JournalJournal of Algebra and its Applications
Volume16
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • commutative differential algebra
  • Gelfand-Dorfman-Novikov algebra
  • Gröbner-Shirshov basis
  • word problem
  • LIE-ALGEBRAS
  • MODULES
  • CALCULUS
  • HAMILTONIAN OPERATORS
  • CHARACTERISTIC-0
  • Grobner-Shirshov basis

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