Geodesic
$\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 355-372

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DOI

We introduce the concept of a $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$-Rota–Baxter operator, as a twisted version of a Rota–Baxter operator of weight zero. We show how to obtain a certain $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$-Rota–Baxter operator from a solution of the associative (Bi)Hom-Yang–Baxter equation, and, in a compatible way, a Hom-pre-Lie algebra from an infinitesimal Hom-bialgebra.
DOI : 10.4153/CMB-2018-028-8
Mots-clés : Rota–Baxter operator, Hom-pre-Lie algebra, infinitesimal Hom-bialgebra, associative (Bi)Hom-Yang–Baxter equation 
Liu, Ling; Makhlouf, Abdenacer; Menini, Claudia; Panaite, Florin. $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 355-372. doi: 10.4153/CMB-2018-028-8
@article{10_4153_CMB_2018_028_8,
     author = {Liu, Ling and Makhlouf, Abdenacer and Menini, Claudia and Panaite, Florin},
     title = {$\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}${-Rota{\textendash}Baxter} {Operators,} {Infinitesimal} {Hom-bialgebras} and the {Associative} {(Bi)Hom-Yang{\textendash}Baxter} {Equation}},
     journal = {Canadian mathematical bulletin},
     pages = {355--372},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/CMB-2018-028-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-028-8/}
}
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AU  - Liu, Ling
AU  - Makhlouf, Abdenacer
AU  - Menini, Claudia
AU  - Panaite, Florin
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JO  - Canadian mathematical bulletin
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%A Makhlouf, Abdenacer
%A Menini, Claudia
%A Panaite, Florin
%T $\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation
%J Canadian mathematical bulletin
%D 2019
%P 355-372
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%R 10.4153/CMB-2018-028-8
%F 10_4153_CMB_2018_028_8

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