Abstract
Following V. Drinfeld and G. Olshansky, we construct Manin triples (g, a, a *) such that g is different from Drinfeld's doubles of a for several series of Lie superalgebras a which have no even invariant bilinear form (periplectic, Poisson and contact) and for a remarkable exception.Straightforward superization of suitable Etingof-Kazhdan's results guarantee then the uniqueness of q-quantization of our Lie bialgebras.Our examples give solutions to the quantum Yang-Baxter equation in the cases when the classical YB equation has no solutions.To find explicit solutions is a separate (open) problem.It is also an open problem to list (à la Belavin-Drinfeld) all solutions of the classical YB equation for the Poisson superalgebras po(0|2n) and the exceptional Lie superalgebra k (1|6) which has a Killing-like supersymmetric bilinear form but no Cartan matrix.