RESEARCH ARTICLE

J-dendriform algebras

  • Dongping HOU 1,2 ,
  • Chengming BAI , 1
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  • 1. Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, China
  • 2. Department of Mathematics, Yunnan Normal University, Kunming 650092, China

Received date: 29 Dec 2009

Accepted date: 21 Sep 2011

Published date: 01 Feb 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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.

Cite this article

Dongping HOU , Chengming BAI . J-dendriform algebras[J]. Frontiers of Mathematics in China, 0 , 7(1) : 29 -49 . DOI: 10.1007/s11464-011-0160-7

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