Abstract
Rota-Baxter operators or relations were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. In this paper, we commence to study the Rota-Baxter operators of weight zero on pre-Lie algebras. Such operators satisfy (the operator form of) the classical Yang-Baxter equation on the sub-adjacent Lie algebras of the pre-Lie algebras. We not only study the invertible Rota-Baxter operators on pre-Lie algebras, but also give some interesting construction of Rota-Baxter operators. Furthermore, we give all Rota-Baxter operators on 2-dimensional complex pre-Lie algebras and some examples in higher dimensions.
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