Totally compatible associative and Lie dialgebras,tridendriform algebras and PostLie algebras  

作　　者：ZHANG Yong BAI ChengMing GUO Li 

机构地区：[1]Department of Mathematics,Zhejiang University [2]Chern Institute of Mathematics & LPMC,Nankai University [3]Department of Mathematics,Lanzhou University [4]Department of Mathematics and Computer Science,Rutgers University

出　　处：《Science China Mathematics》2014年第2期259-273,共15页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10920161,11271202,11221091 and 11371178);Specialized Research Fund for the Doctoral Program of Higher Education(Grant Nos.200800550015 and 20120031110022);National Science Foundation of USA(Grant No.DMS-1001855)

摘　　要：This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.

关 键 词：totally compatible algebra Rota-Baxter operator tridendriform algebra PostLie algebra 

分 类 号：O152.5[理学—数学] TP306.3[理学—基础数学]