Representations via differential algebras and equationally Noetherian algebras

2023/01/17 by Mikhalev, Alexander A., Mustafa, Manat, Umirbaev, Ualbai
#12H05 #16P40 #17A50 #17B63 #17B66 #17D25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2301.06693

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.

Related

• Polynomial representations of the Witt Lie algebra
• Direct products, varieties, and compactness conditions
• Transposed Poisson structures on Witt-type algebras
• Automorphisms and derivations of a universal left-symmetric enveloping algebra
• Equational Noetherian Algebras and Chain Conditions