Geodesic
Group extensions, fiber bundles, and a~parametric Yang--Baxter equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 310-318

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We show that any extension of an Abelian group corresponds to a solution of the parametric Yang–Baxter equation. This statement is a generalization of the well-known construction of a braided set in terms of group structure to the case of group extensions. We also show that this construction in the case of a semidirect product is a specialization of a more general construction using principal bundles and that the case of vector bundles considered earlier is an infinitesimal version of the case of a solution coming from the principal bundle structure.
Keywords: parametric Yang–Baxter equation, group extension, principal bundle, shelf. 
@article{TMF_2021_207_2_a9,
     author = {M. M. Preobrazhenskaya and D. V. Talalaev},
     title = {Group extensions, fiber bundles, and a~parametric {Yang--Baxter} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {310--318},
     publisher = {mathdoc},
     volume = {207},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a9/}
}
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M. M. Preobrazhenskaya; D. V. Talalaev. Group extensions, fiber bundles, and a~parametric Yang--Baxter equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 310-318. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a9/