I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2005, VOLUME 11, NUMBER 2, PAGES 185-208
The quantum double of the Yangian of the Lie superalgebra
and computation of the universal
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The Yangian double of the Lie
superalgebra is described in
terms of generators and defining relations.
We prove the triangular decomposition for Yangian and its quantum
a corollary of the PBW theorem.
We introduce normally ordered bases in the Yangian and its dual Hopf
superalgebra in the quantum double.
We calculate the pairing formulas between the elements of these bases.
We obtain the formula for the universal -matrix of the Yangian
The formula for the universal -matrix of the Yangian,
which was introduced by V. Drinfel'd, is also obtained.
Last modified: June 9, 2005