The Yangian double of the Lie superalgebra \(A(m,n)\) (Q2498301)

The Yangian double \(DY(A(m, n))\) of the Lie superalgebra \(A(m, n)\) is described in terms of generators and defining relations. Normally ordered bases in the Yangian and its dual in the quantum double are introduced. We calculate the pairing between the elements of these bases and obtain a formula for the universal \(R\)-matrix of the Yangian double as well as a formula for the universal \(R\)-matrix (introduced by Drinfeld) of the Yangian. This paper is a continuation of the author's article [Funct. Anal. Appl. 28, No. 3, 217--219 (1994); translation from Funkts. Anal. Prilozh. 28, No. 3, 85--88 (1994; Zbl 0862.17011 )]. A detailed exposition of the results announced in the paper under review was given in Fundam. Prikl. Mat. 11, No. 2, 185--208 (2005); translation in J. Math. Sci., New York 142, No. 2, 1989--2006 (2007; Zbl 1072.17008).