FUNDAMENTALNAYA
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
$A(m,n)$ and computation of the universal
$R$-matrix**

V.
A.
Stukopin

Abstract

View as HTML
View as gif image

The Yangian double $DY(A(m,n))$ of the Lie
superalgebra $A(m,n)$ is described in
terms of generators and defining relations.
We prove the triangular decomposition for Yangian $Y(A(m,n))$ and its quantum
double $DY(A(m,n))$ as
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 $R$-matrix of the Yangian
double.
The formula for the universal $R$-matrix of the Yangian,
which was introduced by V. Drinfel'd, is also obtained.

Location: http://mech.math.msu.su/~fpm/eng/k05/k052/k05213h.htm

Last modified: June 9, 2005