Representations via differential algebras and equationally Noetherian algebras

Alexander A. Mikhalev, Manat Mustafa, Ualbai Umirbaev

Research output: Contribution to journalArticlepeer-review


We show that free algebras of the variety of algebras generated by the Witt algebra Wn, the left-symmetric Witt algebra Ln, and the symplectic Poisson algebra Pn can be described as subalgebras of differential polynomial algebras with respect to appropriately defined products. Using these representations, we prove that Wn, Ln, Pn, and the free algebras of the varieties of algebras generated by these algebras are equationally Noetherian.

Original languageEnglish
Pages (from-to)814-830
Number of pages17
JournalJournal of Algebra
Publication statusPublished - Nov 1 2023


  • Differential algebras
  • Equationally Noetherian algebras
  • Left-symmetric algebras
  • Lie algebras
  • Poisson algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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