Lie algebroid structures on C^∞(M, g) induce Poisson brackets on C^∞(M × g*) that include but strictly exceed the Darboux and Lie-Poisson cases, with computational examples and central extensions studied.
Choquet–Bruhat, C, deWitt–Morette with M
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On Poisson structures arising from a Lie group action
Lie algebroid structures on C^∞(M, g) induce Poisson brackets on C^∞(M × g*) that include but strictly exceed the Darboux and Lie-Poisson cases, with computational examples and central extensions studied.