论文标题
SU（2）Lie-Poisson代数及其后代
The SU(2) Lie-Poisson Algebra and its Descendants
论文作者
论文摘要
在本文中，提出了一个新颖的离散代数，该代数将结合了SU（2）Lie-Poisson支架与离散的FRENET方程。从物理上讲，构造描述了R3中的离散分段线性字符串。我们派生的起点是在字符串的每个顶点分配的离散FRENET帧。然后连接相邻顶点的链接向量分配了SU（2）Lie-Poisson支架。此外，相同的括号定义了离散FRENET方程的传输矩阵，该方程将沿字符串的两个相邻帧相关联。该过程以自相似的方式扩展到泊松结构的无限层次结构。例如，详细介绍了SU（2）Lie-Poisson结构的第一个后代。为此，使用离散FRENET方程的旋转表示，因为它将括号转换为计算更易于管理的形式。最终结果是一种非线性，非平凡和新颖的泊松结构，它与四个相邻的顶点相关。
In this paper, a novel discrete algebra is presented which follows by combining the SU(2) Lie-Poisson bracket with the discrete Frenet equation. Physically, the construction describes a discrete piecewise linear string in R3. The starting point of our derivation is the discrete Frenet frame assigned at each vertix of the string. Then the link vector that connect the neighbouring vertices assigns the SU(2) Lie-Poisson bracket. Moreover, the same bracket defines the transfer matrices of the discrete Frenet equation which relates two neighbouring frames along the string. The procedure extends in a self-similar manner to an infinite hierarchy of Poisson structures. As an example, the first descendant of the SU(2) Lie-Poisson structure is presented in detail. For this, the spinor representation of the discrete Frenet equation is employed, as it converts the brackets into a computationally more manageable form. The final result is a nonlinear, nontrivial and novel Poisson structure that engages four neighbouring vertices.
