Yangian of the Queer Lie Superalgebra

Abstract:

Consider the complex matrix Lie superalgebra with the standard generators , where . Define an involutory automorphism η of by . The twisted polynomial current Lie superalgebra

has a natural Lie co-superalgebra structure. We quantise the universal enveloping algebra as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld. We also construct a wide class of irreducible representations of the quantised algebra.