Triangular structures on flat Lie algebras

Amine Bahayou

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arXiv · 2203.15067

Triangular structures on flat Lie algebras

Amine Bahayou

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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.

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Amine Bahayou. 2022-03-28. Triangular structures on flat Lie algebras. https://arxiv.org/abs/2203.15067

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