AI 中文总结
该研究对辛型六维实幂零李双代数进行分类，获取相关泊松-李群的泊松结构，并得到以泊松-李群为相空间、其对偶李群为对称群的新可积哈密顿系统。
AI 中文摘要
本文对所有辛型六维实幂零李双代数进行了分类。得到了所有相关六维泊松-李群上的泊松结构。还得到了一些新的可积哈密顿系统，其中泊松-李群作为相空间，其对偶李群作为系统的对称群。
英文摘要
In this paper, we classify all six-dimensional real nilpotent Lie bialgebras of symplectic type. The Poisson structures on all of the related six-dimensional Poisson-Lie groups are obtained. Some new integrable Hamiltonian systems for which the Poisson-Lie group plays the role of a phase space and its dual Lie group plays the role of a symmetry group of the system are obtained.
