The Rota‐Baxter Algebra Structures on Split Semiquaternion Algebra
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DOI: 10.1002/mma.11218
Abstract: In this paper, we shall describe all the Rota‐Baxter operators with any weight on split semiquaternion algebra. Firstly, we give the matrix characterization of the Rota‐Baxter operator on split semiquaternion algebra. Then we give the… read more here.
Keywords: split semiquaternion; semiquaternion algebra; rota baxter; algebra ... See more keywords
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
Free Rota-Baxter systems and a Hopf algebra structure
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DOI: 10.1080/00927872.2018.1427246
Abstract: ABSTRACT In this paper, we give a linear basis of a free Rota-Baxter system on a set by using the Gröbner-Shirshov bases method and then we obtain a Hopf algebra structure on a free Rota-Baxter… read more here.
Keywords: algebra structure; free rota; rota baxter; hopf algebra ... 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
Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects
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DOI: 10.1080/00927872.2023.2212775
Abstract: Groups with various types of operators, in particular the recently introduced Rota-Baxter groups, have generated renowned interest with close connections to numerical integrals, Yang-Baxter equation, integrable systems and post-Hopf algebras. This paper gives the general… read more here.
Keywords: rota baxter; groups differential; baxter groups; operated groups ... See more keywords
Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras
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DOI: 10.1142/s0219498817501900
Abstract: We generalize the Lyndon–Shirshov words to the Lyndon–Shirshov Ω-words on a set X and prove that the set of all the nonassociative Lyndon–Shirshov Ω-words forms a linear basis of the free Lie Ω-algebra on the… read more here.
Keywords: shirshov bases; lie; lie algebras; rota baxter ... See more keywords
Braided Rota–Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras
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DOI: 10.1142/s0219498822501341
Abstract: Rota–Baxter algebras and the closely related dendriform algebras have important physics applications, especially to renormalization of quantum field theory. Braided structures provide effective ways of quantization such as for quantum groups. Continuing recent study relating… read more here.
Keywords: rota baxter; baxter algebras; dendriform; algebras braided ... See more keywords
Matching Rota-Baxter Systems and Gröbner-Shirshov Bases
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DOI: 10.1142/s1005386724000294
Abstract: Motivated by the concept of matching Rota-Baxter algebras arising from polarized associative Yang-Baxter equations and Volterra integral equations, we introduce the notion of a matching Rota-Baxter system, which generalizes the Rota-Baxter system proposed by Brzeziński.… read more here.
Keywords: rota baxter; baxter; baxter systems; bner shirshov ... See more keywords
Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators
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DOI: 10.1515/forum-2023-0268
Abstract: Abstract We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang–Baxter equation (CLYBE) whose skew-symmetric parts are invariant. In addition to triangular Leibniz bialgebras, quasi-triangular Leibniz… read more here.
Keywords: rota baxter; factorizable leibniz; leibniz; leibniz bialgebras ... 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