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arXiv · 2301.06693

Representations via differential algebras and equationally Noetherian algebras

Alexander A. Mikhalev·Manat Mustafa·Ualbai Umirbaev
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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.

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Alexander A. Mikhalev, Manat Mustafa, Ualbai Umirbaev. 2023-01-17. Representations via differential algebras and equationally Noetherian algebras. https://arxiv.org/abs/2301.06693

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