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On the free metabelian Novikov and metabelian Lie-admissible algebras (2401.06993v3)
Published 13 Jan 2024 in math.RA
Abstract: In this paper, we consider Lie-admissible algebras, which are free Novikov and free Lie-admissible algebras with an additional metabelian identity. We construct a linear basis for both free metabelian Novikov and free metabelian Lie-admissible algebras. Additionally, we describe a space of symmetric polynomials for both the free metabelian Novikov algebra and the free metabelian Lie-admissible algebra.