J-dendriform algebras
Received date: 29 Dec 2009
Accepted date: 21 Sep 2011
Published date: 01 Feb 2012
Copyright
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.
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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