Injective Rota–Baxter Operators of Weight Zero on F[x]
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DOI: 10.1007/s00009-021-01909-z
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 $\mathbb{R}[x]$… read more here.
Keywords: baxter operators; weight zero; rota; injective rota ... See more keywords
Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three
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DOI: 10.1007/s00009-024-02744-8
Abstract: We describe all Rota–Baxter operators R of weight zero on the algebra U3(F)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U_3(F)$$\end{document} of upper-triangular matrices of order three over a field of characteristic 0. For… read more here.
Keywords: rota baxter; baxter operators; upper triangular; weight zero ... See more keywords
Classification of Rota-Baxter operators on semigroup algebras of order two and three
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DOI: 10.1080/00927872.2018.1552278
Abstract: Abstract In this paper, we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators… read more here.
Keywords: algebras order; baxter operators; semigroup algebras; order two ... See more keywords
Rota-Baxter operators on filiform Lie algebras L3 and L4
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DOI: 10.2989/16073606.2025.2475235
Abstract: Abstract In this paper, we completely determine all the Rota-Baxter operators on the 3-dimensional filiform Lie algebra and the 4-dimensional filiform Lie algebra . As an application of Rota-Baxter operators, we derive the skew-symmetric solutions… read more here.
Keywords: rota baxter; baxter; baxter operators; algebra ... See more keywords
Rota–Baxter Operators on Skew Braces
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DOI: 10.3390/math12111671
Abstract: In this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as (Z,+,∘) and (Z/(4),+,∘). We also present a necessary and sufficient condition for… read more here.
Keywords: rota baxter; operators skew; skew braces; baxter ... See more keywords