杨代数

若a是半单李代数，Y(a)是无限维的霍普夫代数（跟泛包络代数有关系）。Y(a)是杨代数。

有些方程

${\displaystyle [t_{ij}^{(p+1)},t_{kl}^{(q)}]-[t_{ij}^{(p)},t_{kl}^{(q+1)}]=-(t_{kj}^{(p)}t_{il}^{(q)}-t_{kj}^{(q)}t_{il}^{(p)}).}$ 

若${\displaystyle t_{ij}^{(-1)}=\delta _{ij}}$ 

${\displaystyle T(z)=\sum _{p\geq -1}t_{ij}^{(p)}z^{-p+1}}$ 

若R-矩阵是 R(z)= I+ z^-1 P

${\displaystyle \displaystyle {R_{12}(z-w)T_{1}(z)T_{2}(w)=T_{2}(w)T_{1}(z)R_{12}(z-w).}}$ 

${\displaystyle (\Delta \otimes \mathrm {id} )T(z)=T_{12}(z)T_{13}(z),\,\,(\varepsilon \otimes \mathrm {id} )T(z)=I,\,\,(s\otimes \mathrm {id} )T(z)=T(z)^{-1}.}$ 

${\displaystyle \displaystyle {S(z)=T(z)\sigma T(-z),}}$ 

${\displaystyle \displaystyle {\sigma (E_{ij})=(-1)^{i+j}E_{2N-j+1,2N-i+1}.}}$ 

• 杨–巴克斯特方程
• 超对称杨–米尔斯理论^[1][2]

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