Triangular structures on flat Lie algebras
Differential Geometry
2022-09-20 v2
Abstract
In this work 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 \emph{exact metaflat Lie bialgebras}. We give a complete classification of these structures. We show that given the metaflatness geometrical condition, these exact bialgebra structures arise necessarily from a nontrivial solution of the classical Yang-Baxter equation. Moreover, the dual Lie bialgebra is also flat and metaflat constituting an important kind of symmetry.
Cite
@article{arxiv.2203.15067,
title = {Triangular structures on flat Lie algebras},
author = {Amine Bahayou},
journal= {arXiv preprint arXiv:2203.15067},
year = {2022}
}