Volume 14, Issue 2, April 2007, Pages 269 - 289
Rota-Baxter operators on pre-Lie algebras
- Xiuxian LI, Dongping HOU, Chengming BAI
- Corresponding Author
- Xiuxian LI
Available Online 2 April 2007.
- https://doi.org/10.2991/jnmp.2007.14.2.9How to use a DOI?
- Rota-Baxter operators or relations were introduced to solve certain analytic and com- binatorial 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 classi- cal 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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Cite this article
TY - JOUR AU - Xiuxian LI AU - Dongping HOU AU - Chengming BAI PY - 2007 DA - 2007/04 TI - Rota-Baxter operators on pre-Lie algebras JO - Journal of Nonlinear Mathematical Physics SP - 269 EP - 289 VL - 14 IS - 2 SN - 1402-9251 UR - https://doi.org/10.2991/jnmp.2007.14.2.9 DO - https://doi.org/10.2991/jnmp.2007.14.2.9 ID - LI2007 ER -