Compatible Lie Bialgebras  

作　　者：吴明忠 白承铭 

机构地区：[1]Chern Institute of Mathematics & LPMC,Nankai University

出　　处：《Communications in Theoretical Physics》2015年第6期653-664,共12页理论物理通讯（英文版）

基　　金：Supported by National Natural Science Foundation of China under Grant Nos.11271202,11221091,11425104;Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20120031110022

摘　　要：A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie Mgebras as an analogue of a piiLie bialgebra. They can also be regarded as a ＂compatible version＂ of Lie bialgebras, that is, a pair of Lie biaJgebras such that any linear combination of the two Lie bialgebras is still a Lie bialgebra. Many properties of compatible Lie bialgebras as the ＂compatible version＂ of the corresponding properties of Lie biaJgebras are presented. In particular, there is a coboundary compatible Lie bialgebra theory with a construction from the classical Yang-Baxter equation in compatible Lie algebras as a combination of two classical Yang-Baxter equations in lAe algebras. FUrthermore, a notion of compatible pre-Lie Mgebra is introduced with an interpretation of its close relation with the classical Yang-Baxter equation in compatible Lie a/gebras which leads to a construction of the solutions of the latter. As a byproduct, the compatible Lie bialgebras fit into the framework to construct non-constant solutions of the classical Yang-Baxter equation given by Golubchik and Sokolov.

关 键 词：compatible Lie algebra Lie bialgebra classical Yang-Baxter equation pre-Lie algebra 

分 类 号：O152.5[理学—数学] O413.1[理学—基础数学]