变形反对称矩阵空间上的Lie丛
Lie bundle on the space of deformed skew-symmetric matrices
摘要：
研究了变形反对称$n \times n$矩阵的李代数$\mathcal A_{a_1,\ldots,a_{n-1}}$，通过选择变形对称矩阵赋予它一个李括号.变形由实数序列$a_1,\ldots,a_{n-1}$参数化。利用同构$\mathcal A_{a_1,\ldots,a_{n-1}}^* \cong L_+$在上三角矩阵空间$L_+$上引入了Lie-Poisson结构.用这种方法，我们生成了具有双哈密顿结构的Hamilton系统的族。
英文摘要：
We study a Lie algebra $\mathcal A_{a_1,\ldots,a_{n-1}}$ of deformed skew-symmetric $n \times n$ matrices endowed with a Lie bracket given by a choice of deformed symmetric matrix. The deformations are parametrized by a sequence of real numbers $a_1,\ldots,a_{n-1}$. Using isomorphism $\mathcal A_{a_1,\ldots,a_{n-1}}^* \cong L_+$ we introduce a Lie-Poisson structure on the space of upper-triangular matrices $L_+$. In this way we generate hierarchies of Hamilton systems with bihamiltonian structure.
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