与李括号线性丛相关的李代数扩张
Lie algebra extensions related with linear bundles of Lie brackets
摘要：
考虑了$({\cal G}^*)^n$上的Lie-Poisson结构理论中出现的任意李代数${\cal G}$的一些特殊类型扩张，其中${\cal G}^*$是${\cal G}$的对偶.我们证明了这些扩张的某些类可以用李代数的线性丛以自然的方式构造。
英文摘要：
We consider some special type extensions of an arbitrary Lie algebra ${\cal G}$, arising in the theory of Lie-Poisson structures over $({\cal G}^*)^n$, where ${\cal G}^*$ is the dual of ${\cal G}$. We show that some classes of these extensions can be constructed in a natural way using some linear bundles of Lie algebras.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
