On the free metabelian Novikov and metabelian Lie-admissible algebras

2024

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DOI 10.46298/cm.12877
Data confidence 70 medium
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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.