Work

A Non-linearizable Action of $S_3$ on Free Metabelian Lie and Associative Algebras

Year: 2026

Type: preprint

Abstract: Let $M$ be the free metabelian Lie algebra of rank $4$ over the field of complex numbers $\mathbb{C}$. We construct a non-linearizable action of the symmetric group $S_3$, the smallest nonabelian group, on $M$ by automorphisms. We also construct a non-linearizable action of $S_3$ on free metabelian associative algebras of rank $4$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26060

Authors: Naurazbekova, Altyngul, Umirbaev, Ualbai

Institutions: L. N. Gumilyov Eurasian National University, Wayne State University, Al-Farabi Kazakh National University

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223047011

Cites: 1

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Related to: 10