On the free metabelian Novikov and metabelian Lie-admissible algebras

Aigerim Dauletiyarova; Kanat Abdukhalikov; Bauyrzhan Sartayev

doi:10.46298/cm.12877

On the free metabelian Novikov and metabelian Lie-admissible algebras

Aigerim Dauletiyarova, Kanat Abdukhalikov, Bauyrzhan Sartayev

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Journal	Communications in Mathematics
Volume	33
Issue number	3 Special issue
DOIs	https://doi.org/10.46298/cm.12877
Publication status	Published - 2025

Keywords

Lie-admissible algebra
Novikov algebra
free algebra
metabelian identity
polynomial identities

ASJC Scopus subject areas

General Mathematics

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10.46298/cm.12877

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AB - 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.

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KW - Novikov algebra

KW - free algebra

KW - metabelian identity

KW - polynomial identities

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On the free metabelian Novikov and metabelian Lie-admissible algebras

Abstract

Keywords

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