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arXiv · 2403.13697

Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures

Maxim Goncharov
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Abstract

In the paper, we introduce the notion of a Rota-Baxter operator of a non-scalar weight. As a motivation, we show that there is a natural connection between Rota-Baxter operators of this type and structures of quasitriangular Lie bialgebras on a quadratic finite-dimensional Lie algebra. Moreover, we show that some classical results on Lie bialgebra structure on simple finite-dimensional Lie algebras can be obtained from the corresponding results for Rota-Baxter operators.

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BibTeXRIS

Maxim Goncharov. 2024-03-20. Rota-Baxter operators of non-scalar weights, connections with coboundary Lie bialgebra structures. https://arxiv.org/abs/2403.13697

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