Representations via differential algebras and equationally Noetherian algebras

Abstract

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.