Polyubles of pre-Lie bialgebras

The notion of polyubles of a pre-Lie bialgebra is introduced as a generalization of the symplectic double. They are pre-Lie bialgebras for which the 2 k -ubles are factorizable. In particular, in the case of a quasi-triangular pre-Lie bialgebra, we construct a new series of pre-Lie bialgebras and establish their relation with polyubles.