Journal of Lie Theory 33 (2023), No. 3, 875--886
Copyright Heldermann Verlag 2023
Triangular Structures on Flat Lie Algebras
Amine Bahayou
Dept. of Mathematics, Kasdi Merbah University, Ouargla, Algeria
amine.bahayou@gmail.com
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.
Keywords: Lie bialgebra, Poisson-Lie group, Yang-Baxter equation.
MSC: 17B38, 17B62, 53D17.
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