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arXiv · 2608.12981

Injective Rota-Baxter operators of weight 1 on $F[x]$

Vsevolod Gubarev
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Abstract

We describe all injective Rota-Baxter operators $R$ of weight 1 on the polynomial algebra $F[x]$. When $\mathrm{char}\,F = p>0$, the only one is $R=-\mathrm{id}$. When $\mathrm{char}\,F = 0$, we have either $R = -\mathrm{id}$ or, up to conjugation with automorphisms of $F[x]$, $R(1) = x$, and $R$ is uniquely defined via this equality. Together with the known weight-zero case, this completes the classification of injective Rota-Baxter operators of any weight on $F[x]$.

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Vsevolod Gubarev. 2026-08-13. Injective Rota-Baxter operators of weight 1 on $F[x]$. https://arxiv.org/abs/2608.12981

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