On the free metabelian Novikov and metabelian Lie-admissible algebras

Authors:
  • ADA. Dauletiyarova
    A. Dauletiyarova
  • KAK. Abdukhalikov
    K. Abdukhalikov
  • BSB. K. Sartayev
    B. K. Sartayev
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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.