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This article is cited in 3 scientific papers (total in 3 papers)
Group extensions, fiber bundles, and a parametric Yang–Baxter equation
M. M. Preobrazhenskayaa, D. V. Talalaevabc a Centre of Integrable Systems, Demidov Yaroslavl State
University, Yaroslavl, Russia
b Mechanics and Mathematics Faculty, Lomonosov Moscow State
University, Russia
c Alikhanov Institute of Theoretical and Experimental
Physics, Moscow, Russia
Abstract:
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.
Received: 07.12.2020 Revised: 10.01.2021
Citation:
M. M. Preobrazhenskaya, D. V. Talalaev, “Group extensions, fiber bundles, and a parametric Yang–Baxter equation”, TMF, 207:2 (2021), 310–318; Theoret. and Math. Phys., 207:2 (2021), 670–677
Linking options:
https://www.mathnet.ru/eng/tmf10022https://doi.org/10.4213/tmf10022 https://www.mathnet.ru/eng/tmf/v207/i2/p310
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Abstract page: | 221 | Full-text PDF : | 35 | References: | 47 | First page: | 17 |
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