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Embedding dendriform algebra into its universal enveloping Rota-Baxter algebra


Authors: Yuqun Chen and Qiuhui Mo
Journal: Proc. Amer. Math. Soc. 139 (2011), 4207-4216
MSC (2010): Primary 13P10, 16S15; Secondary 16W99, 17A50
Published electronically: April 26, 2011
MathSciNet review: 2823066
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Abstract: In this paper, by using Gröbner-Shirshov bases for Rota-Baxter algebras, we prove that every dendriform algebra over a field of characteristic 0 can be embedded into its universal enveloping Rota-Baxter algebra.


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Additional Information

Yuqun Chen
Affiliation: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People’s Republic of China
Email: yqchen@scnu.edu.cn

Qiuhui Mo
Affiliation: School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People’s Republic of China
Email: scnuhuashimomo@126.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10889-X
Keywords: Gröbner-Shirshov basis, universal enveloping algebra, dendriform algebra, Rota-Baxter algebra
Received by editor(s): April 20, 2010
Received by editor(s) in revised form: August 27, 2010, and October 20, 2010
Published electronically: April 26, 2011
Additional Notes: The first author was supported in part by the NNSF of China (Nos. 10771077, 10911120389) and the NSF of Guangdong Province (No. 06025062).
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2011 American Mathematical Society