Riemann-Poisson Lie algebras are characterized by a Kähler Lie subalgebra plus two compatibility conditions, and classified up to dimension five.
Boucetta, On the Riemann-Lie algebras and Riemann-Po isson Lie groups, Journal of Lie Theory
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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.