Volume 14, Issue 2, April 2007, Pages 269 - 289
Rota-Baxter operators on pre-Lie algebras
Authors
Xiuxian Li, Dongping Hou, Chengming Bai
Corresponding Author
Xiuxian Li
Received 15 September 2006, Accepted 14 December 2006, Available Online 1 April 2007.
- DOI
- 10.2991/jnmp.2007.14.2.9How to use a DOI?
- Abstract
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.
- Copyright
- © 2007, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Xiuxian Li AU - Dongping Hou AU - Chengming Bai PY - 2007 DA - 2007/04/01 TI - Rota-Baxter operators on pre-Lie algebras JO - Journal of Nonlinear Mathematical Physics SP - 269 EP - 289 VL - 14 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2007.14.2.9 DO - 10.2991/jnmp.2007.14.2.9 ID - Li2007 ER -