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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.