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arXiv · 2610.26060

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

Altyngul Naurazbekova·Ualbai Umirbaev
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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 $4$.

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Altyngul Naurazbekova, Ualbai Umirbaev. 2026-10-19. A Non-linearizable Action of $S_3$ on Free Metabelian Lie and Associative Algebras. https://arxiv.org/abs/2610.26060

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