Representations via differential algebras and equationally Noetherian algebras

Alexander A. Mikhalev, Manat Mustafa, Ualbai Umirbaev

Research output: Working paperPreprint

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Abstract

We show that free algebras of the variety of algebras generated by the Witt algebra $W_n$, the left-symmetric Witt algebra $L_n$, and the symplectic Poisson algebra $P_n$ can be described as subalgebras of differential polynomial algebras with respect to appropriately defined products. Using these representations, we prove that $W_n$, $L_n$, $P_n$, and the free algebras of the varieties of algebras generated by these algebras are equationally Noetherian.
Original languageEnglish
Publication statusPublished - Jan 17 2023

Keywords

  • math.RA
  • math.AG
  • 12H05, 17B63, 17B66, 17D25, 16P40, 17A50

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