TY - UNPB

T1 - Representations via differential algebras and equationally Noetherian algebras

AU - Mikhalev, Alexander A.

AU - Mustafa, Manat

AU - Umirbaev, Ualbai

N1 - 14 pages

PY - 2023/1/17

Y1 - 2023/1/17

N2 - 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.

AB - 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.

KW - math.RA

KW - math.AG

KW - 12H05, 17B63, 17B66, 17D25, 16P40, 17A50

M3 - Preprint

BT - Representations via differential algebras and equationally Noetherian algebras

ER -