Riemann-Poisson Lie algebras are characterized by a Kähler Lie subalgebra plus two compatibility conditions, and classified up to dimension five.
Boucetta, Riemann-Poisson manifolds and K¨ ahler-Ri emann foliations, C
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On Riemann-Poisson Lie groups
Riemann-Poisson Lie algebras are characterized by a Kähler Lie subalgebra plus two compatibility conditions, and classified up to dimension five.