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

2005/04/14 by V. Stukopin, Stukopin, V.
Mathematics · #17B37(Primary) #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/0504302

22 pages

arxiv created 2005/04/14 · arxiv updated 2009/12/01

Abstract

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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