Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

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

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.

[ Fulltext-pdf  (117  KB)] for subscribers only.