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
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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
14 - 2
Pages
269 - 289
Publication Date
2007/04/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2007.14.2.9How to use a DOI?
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  -