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Journal of Lie Theory 28 (2018), No. 2, 499--524
Copyright Heldermann Verlag 2018

Hawkins Compatibility Conditions on the Tangent Bundle of a Poisson-Lie Group

Foued Aloui
Higher School of Sciences and Technology, Street Lamine Abassi BP 4011, Hammam Sousse, Tunisia

Nadhem Zaalani
Higher Institute of Applied Sciences and Technology, Street Tahar Ben Achour BP 4003, Sousse, Tunisia

Let G be a Poisson-Lie group equipped with a left invariant Riemannian metric compatible with the Poisson structure on G. There are many ways to lift the Poisson structure and the metric to the tangent bundle TG of G. In this paper, we study in different cases the compatibility between the lifted Poisson structure and the lifted metric on TG.

Keywords: Poisson geometry, Riemannian geometry, Lie group, Lie algebra.

MSC: 53D17, 58B20, 70G65

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