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

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

2005-04-14

arxiv.org/abs/math/0504302v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

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

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