Journal of Lie Theory

no. 2
Hawkins Compatibility Conditions on the Tangent Bundle of a Poisson-Lie Group
Foued Aloui1; Nadhem Zaalani2
1Higher School of Sciences and Technology, Street Lamine Abassi BP 4011, Hammam Sousse, Tunisia
2Higher Institute of Applied Sciences and Technology, Street Tahar Ben Achour BP 4003, Sousse, Tunisia
Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 499-524
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.
DOI: 10.5802/jolt.1011
Classification: 53D17, 58B20, 70G65
Keywords: Poisson geometry, Riemannian geometry, Lie group, Lie algebra

Foued Aloui  1 ; Nadhem Zaalani  2

1 Higher School of Sciences and Technology, Street Lamine Abassi BP 4011, Hammam Sousse, Tunisia
2 Higher Institute of Applied Sciences and Technology, Street Tahar Ben Achour BP 4003, Sousse, Tunisia 
Foued Aloui; Nadhem Zaalani. Hawkins Compatibility Conditions on the Tangent Bundle of a Poisson-Lie Group. Journal of Lie Theory, Volume 28 (2018) no. 2, pp. 499-524. doi: 10.5802/jolt.1011
@article{JOLT_2018_28_2_a8,
     author = {Foued Aloui and Nadhem Zaalani},
     title = {Hawkins {Compatibility} {Conditions} on the {Tangent} {Bundle} of a {Poisson-Lie} {Group}},
     journal = {Journal of Lie Theory},
     pages = {499--524},
     year = {2018},
     volume = {28},
     number = {2},
     doi = {10.5802/jolt.1011},
     zbl = {1393.53084},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1011/}
}
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