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arXiv · 2005.14030

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

Vsevolod Gubarev·Alexander Perepechko
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Abstract

Rota-Baxter operators present a natural generalisation of integration by parts formula for the integral operator. In 2015, Zheng, Guo, and Rosenkranz conjectured that every injective Rota-Baxter operator of weight zero on the polynomial algebra $\mathbb{R}[x]$ is a composition of the multiplication by a nonzero polynomial and a formal integration at some point. We confirm this conjecture over any field of characteristic zero. Moreover, we establish a structure of an ind-variety on the moduli space of these operators and describe an additive structure of generic modality two on it. Finally, we provide an infinitely transitive action on codimension one subsets.

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Vsevolod Gubarev, Alexander Perepechko. 2020-05-28. Injective Rota-Baxter operators of weight zero on $F[x]$. https://doi.org/10.1007/s00009-021-01909-z

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