Journal of Lie Theory

no. 3
Triangular Structures on Flat Lie Algebras
Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 875-886
We study a large class of exact Lie bialgebras arising from noncommutative deformations of Poisson-Lie groups endowed with a left invariant Riemannian metric. We call these structures triangular metaflat Lie bialgebras. We show that given the metaflatness geometrical condition, these exact bialgebra structures arise necessarily from a solution of the classical Yang-Baxter equation. Moreover, the dual Lie bialgebra is also metaflat constituting an important kind of symmetry.
DOI: 10.5802/jolt.1310
Classification: 17B38, 17B62, 53D17
Keywords: Lie bialgebra, Poisson-Lie group, Yang-Baxter equation 
@article{JOLT_2023_33_3_a9,
     author = {A. Bahayou},
     title = {Triangular {Structures} on {Flat} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {875--886},
     year = {2023},
     volume = {33},
     number = {3},
     doi = {10.5802/jolt.1310},
     zbl = {1548.17025},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1310/}
}
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%J Journal of Lie Theory
%D 2023
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A. Bahayou. Triangular Structures on Flat Lie Algebras. Journal of Lie Theory, Volume 33 (2023) no. 3, pp. 875-886. doi: 10.5802/jolt.1310

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