Geodesic
Compatible Poisson Brackets on Lie Algebras
Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 11-34

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We discuss the relationship between the representation of an integrable system as an $L$-$A$-pair with a spectral parameter and the existence of two compatible Hamiltonian representations of this system. We consider examples of compatible Poisson brackets on Lie algebras, as well as the corresponding integrable Hamiltonian systems and Lax representations. 
@article{MZM_2002_72_1_a1,
     author = {A. V. Bolsinov and A. V. Borisov},
     title = {Compatible {Poisson} {Brackets} on {Lie} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {11--34},
     publisher = {mathdoc},
     volume = {72},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a1/}
}
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A. V. Bolsinov; A. V. Borisov. Compatible Poisson Brackets on Lie Algebras. Matematičeskie zametki, Tome 72 (2002) no. 1, pp. 11-34. http://geodesic.mathdoc.fr/item/MZM_2002_72_1_a1/