J-dendriform algebras

doi:10.1007/s11464-011-0160-7

Front Math Chin

0, Vol.

Issue () : 29-49 https://doi.org/10.1007/s11464-011-0160-7

RESEARCH ARTICLE

J-dendriform algebras

Dongping HOU^1,2, Chengming BAI¹(

)

1. Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, China; 2. Department of Mathematics, Yunnan Normal University, Kunming 650092, China

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Abstract

In this paper, we introduce a notion of J-dendriform algebra with two operations as a Jordan algebraic analogue of a dendriform algebra such that the anticommutator of the sum of the two operations is a Jordan algebra. A dendriform algebra is a J-dendriform algebra. Moreover, J-dendriform algebras fit into a commutative diagram which extends the relationships among associative, Lie, and Jordan algebras. Their relations with some structures such as Rota-Baxter operators, classical Yang-Baxter equation, and bilinear forms are given.

Keywords Jordan algebra dendriform algebra O-operator classical Yang-Baxter equation (CYBE)

Corresponding Author(s): BAI Chengming,Email:baicm@nankai.edu.cn

Issue Date: 01 February 2012

Cite this article:

Dongping HOU,Chengming BAI. J-dendriform algebras[J]. Front Math Chin, 0, (): 29-49.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-011-0160-7
https://academic.hep.com.cn/fmc/EN/Y0/V/I/29

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