Super Poisson–Lie structure on SU(m|n)SU(m|n) via SL(m|n,C)RSL(m|n,C)R

This paper concerns a super Poisson–Lie structure on the real Lie supergroup SU(m|n)SU(m|n). In fact, it turns out that the realification of the complex Lie supergroup SL(m|n,C)SL(m|n,C) is a double of SU(m|n)SU(m|n) i.e. it is endowed with a structure of super Poisson–Lie which brings down on the supergroup SU(m|n)SU(m|n). We show that the dual Poisson–Lie supergroup of SU(m|n)SU(m|n) is s(AN)s(AN). Reciprocally, s(AN)s(AN) inherits a super Poisson–Lie structure from the realification of SL(m|n,C)SL(m|n,C) such that its dual Poisson–Lie supergroup is SU(m|n)SU(m|n).