Geodesic
Triangular Structures on Flat Lie Algebras
Amine Bahayou1
1Dept. of Mathematics, Kasdi Merbah University, Ouargla, Algeria
Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 875-886

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B38, 17B62, 53D17
Mots-clés : Lie bialgebra, Poisson-Lie group, Yang-Baxter equation

Amine Bahayou  1

1 Dept. of Mathematics, Kasdi Merbah University, Ouargla, Algeria 
Amine Bahayou. Triangular Structures on Flat Lie Algebras. Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 875-886. http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a9/
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     title = {Triangular {Structures} on {Flat} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {875--886},
     year = {2023},
     volume = {33},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a9/}
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