Geodesic
The quantum double of the Yangian of the Lie superalgebra $A(m,n)$ and computation of the universal $R$-matrix
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 185-208

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FPM_2005_11_2_a12,
     author = {V. A. Stukopin},
     title = {The quantum double of the {Yangian} of the {Lie} superalgebra $A(m,n)$ and computation of the universal $R$-matrix},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {185--208},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_2_a12/}
}
TY  - JOUR
AU  - V. A. Stukopin
TI  - The quantum double of the Yangian of the Lie superalgebra $A(m,n)$ and computation of the universal $R$-matrix
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2005
SP  - 185
EP  - 208
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2005_11_2_a12/
LA  - ru
ID  - FPM_2005_11_2_a12
ER  - 
%0 Journal Article
%A V. A. Stukopin
%T The quantum double of the Yangian of the Lie superalgebra $A(m,n)$ and computation of the universal $R$-matrix
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2005
%P 185-208
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2005_11_2_a12/
%G ru
%F FPM_2005_11_2_a12
V. A. Stukopin. The quantum double of the Yangian of the Lie superalgebra $A(m,n)$ and computation of the universal $R$-matrix. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 2, pp. 185-208. http://geodesic.mathdoc.fr/item/FPM_2005_11_2_a12/