Quantum Double of Yangian of Lie Superalgebra $A(m,n)$ and computation of Universal $R$-matrix

摘要

Yangian Double $DY(A(m,n))$ of Lie Superalgebra $A(m,n)$ is described interms of generators and defining relations. It is proved triangulardecomposition for Yangian $Y(A(m,n))$ and its quantum double $DY(A(m,n))$ as acorollary of PBW theorem. It is introduced the normally ordered bases inYangian and its dual Hopf superalgebra in quantum double. It is calculated thepairing formulas between the elements of its bases. It is received the formulaof Universal $R$-matrix of Yangian Double. The formula for Universal $R$-matrixof Yangian, which was introduced by V. Drinfel'd, is received also.