Representations via differential algebras and equationally Noetherian algebras
Mikhalev A.A. Mustafa M. Umirbaev U.
1 November 2023Academic Press Inc.
Journal of Algebra
2023#633814 - 830 pp.
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.
Differential algebras , Equationally Noetherian algebras , Left-symmetric algebras , Lie algebras , Poisson algebras
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Faculty of Mechanics and Mathematics, M.V.Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russian Federation
Department of Mathematics, SSH, Nazarbayev University, 53 Kabanbay Batyr Avenue, Astana, 010000, Kazakhstan
Department of Mathematics, Wayne State University, Detroit, 48202, MI, United States
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Faculty of Mechanics and Mathematics
Department of Mathematics
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
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