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We first prove that, for any generalized Hamiltonian type Lie algebra \(\mathcal{H}\), the first cohomology group \(H^1 (\mathcal{H},\mathcal{H} \otimes \mathcal{H})\) is trivial. We then show that all Lie bialgebra structures on \(\mathcal{H}\) are triangular
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This work was supported by the National Natural Science Foundation of China (Grant No. 10471091) and “One Hundred Talents Program” from University of Science and Technology of China
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Xin, B., Song, Ga. & Su, Yc. Hamiltonian type Lie bialgebras. SCI CHINA SER A 50, 1267–1279 (2007). https://doi.org/10.1007/s11425-007-0078-4
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DOI: https://doi.org/10.1007/s11425-007-0078-4