楊代數

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

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

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

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

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

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