摘要
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 antieommutator 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.
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 antieommutator 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.
基金
Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 10621101, 10921061）, the National Key Basic Research Development Project （2006CB805905）, and the Specialized Research Fund for the Doctoral Program （200800550015）.
