关于一个正则动力学r-矩阵的注记
A note on a canonical dynamical r-matrix
摘要：
众所周知，经典动力学$r$ -矩阵可以通过定义$R(ω):= f(\mathrm{ad} ω)$与每个有限维自对偶李代数$\G$相关联，其中$ω\in \G$和$f$是由$f(z)={1/2}\coth \frac{z}{2}-\frac{1}{z}$为$z\in \C\setminus 2πi \Z^*$给出的全纯函数。我们提出了一个新的，直接证明的声明，这规范$r$ -矩阵满足修改后的经典动力学杨-巴克斯特方程$\G$。
英文摘要：
It is well known that a classical dynamical $r$-matrix can be associated with every finite-dimensional self-dual Lie algebra $\G$ by the definition $R(ω):= f(\mathrm{ad} ω)$, where $ω\in \G$ and $f$ is the holomorphic function given by $f(z)={1/2}\coth \frac{z}{2}-\frac{1}{z}$ for $z\in \C\setminus 2πi \Z^*$. We present a new, direct proof of the statement that this canonical $r$-matrix satisfies the modified classical dynamical Yang-Baxter equation on $\G$.
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