Abstract
In this paper, we study pre-Lie analogues of Poisson-Nijenhuis structures and introduce [Formula: see text]-structures on bimodules over pre-Lie algebras. We show that an [Formula: see text]-structure gives rise to a hierarchy of pairwise compatible [Formula: see text]-operators. We study solutions of the strong Maurer–Cartan equation on the twilled pre-Lie algebra associated to an [Formula: see text]-operator, which gives rise to a pair of [Formula: see text]-structures which are naturally in duality. We show that KVN-structures and HN-structures on a pre-Lie algebra [Formula: see text] are corresponding to [Formula: see text]-structures on the bimodule [Formula: see text], and KVB-structures are corresponding to solutions of the strong Maurer–Cartan equation on a twilled pre-Lie algebra associated to an [Formula: see text]-matrix.
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