TY - JOUR
T1 - Representations via differential algebras and equationally Noetherian algebras
AU - Mikhalev, Alexander A.
AU - Mustafa, Manat
AU - Umirbaev, Ualbai
N1 - Funding Information:
The third author is supported by the Ministry of Education and Science of the Republic of Kazakhstan (project AP14872073 ).
Funding Information:
The second author is supported by Nazarbayev University FDCRG (Grant No. 021220FD3851 ).
Funding Information:
The first author is supported by Russian Science Foundation , grant 22-11-00052 .
Publisher Copyright:
© 2023 Elsevier Inc.
PY - 2023/11/1
Y1 - 2023/11/1
N2 - 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.
AB - 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.
KW - Differential algebras
KW - Equationally Noetherian algebras
KW - Left-symmetric algebras
KW - Lie algebras
KW - Poisson algebras
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U2 - 10.1016/j.jalgebra.2023.07.008
DO - 10.1016/j.jalgebra.2023.07.008
M3 - Article
AN - SCOPUS:85165681327
SN - 0021-8693
VL - 633
SP - 814
EP - 830
JO - Journal of Algebra
JF - Journal of Algebra
ER -