Journal of Nonlinear Mathematical Physics

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
Available Online 1 April 2007.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
14 - 2
Pages
269 - 289
Publication Date
2007/04
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2007.14.2.9How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

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  - 1776-0852
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  -