
Journal of Lie Theory 20 (2010), No. 4, 767783 Copyright Heldermann Verlag 2010 The Construction of HomLie Bialgebras Yuanyuan Chen College of Science, Nanjing Agriculture University, Nanjing 210095, P. R. China 2008111010@njau.edu.cn Yong Wang College of Mathematics and Information Technology, Xiaozhuang University, Nanjing 211171, P. R. China wangyongmath@gmail.com Liangyun Zhang College of Science, Nanjing Agriculture University, Nanjing 210095, P. R. China zlyun@njau.edu.cn Motivated by recent literature on HomLie algebras and the construction of Lie bialgebras, we investigate the construction of HomLie bialgebras as a generalization of Lie bialgebras. In this paper, we mainly show how to construct (triangular coboundary) HomLie bialgebras both through HomLie algebras and HomLie coalgebras. As examples, we consider the construction of (triangular coboundary) HomLie bialgebras on the threedimensional Heisenberg algebra, on the split simple Lie algebra sl(2) and on E^{3}, the threedimensional Euclidean space. Keywords: HomLie algebra, HomLie module, HomLie bialgebra, triangular coboundary HomLie bialgebra. MSC: 17B99, 17B37, 16W30 [ Fulltextpdf (279 KB)] for subscribers only. 