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Pre-Jordan Algebras

Hou, Dongping and Ni, Xiang and Bai, Chengming (2013) Pre-Jordan Algebras. Mathematica Scandinavica, 112 (1). pp. 19-48. ISSN 0025-5521.

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The purpose of this paper is to introduce and study a notion of pre-Jordan algebra. Pre-Jordan algebras are regarded as the underlying algebraic structures of the Jordan algebras with a nondcgenerate symplectic form. They are the algebraic structures behind the Jordan Yang-Baxter equation and Rota-Baxter operators in terms of O-operators of Jordan algebras introduced in this paper. Pre-Jordan algebras are analogues for Jordan algebras of pre-Lie algebras and fit into a bigger framework with a close relationship with dendriform algebras. The anticommutator of a pre-Jordan algebra is a Jordan algebra and the left multiplication operators give a representation of the Jordan algebra, which is the beauty of such a structure. Furthermore, we introduce a notion of O-operator of a pre-Jordan algebra which gives an analogue of the classical Yang-Baxter equation in a pre-Jordan algebra.

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Additional Information:© 2013 Institut for Matematik. Received 7 January 2010, in final form 20 April 2010. We thank the referee for the important suggestions. This work was supported in part by the National Natural Science Foundation of China (10621101, 10921061, 11221091), NKBRPC (2006CB805905) and SRFDP (200800550015, 20120031110022).
Funding AgencyGrant Number
National Natural Science Foundation of China10621101
National Natural Science Foundation of China10921061
National Natural Science Foundation of China11221091
Issue or Number:1
Record Number:CaltechAUTHORS:20130819-150100892
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:40723
Deposited By: Tony Diaz
Deposited On:19 Aug 2013 22:15
Last Modified:03 Oct 2019 05:42

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