Journal of Lie Theory 20 (2010), No. 4, 767--783
Copyright Heldermann Verlag 2010
The Construction of Hom-Lie 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 Hom-Lie algebras and the construction of Lie bialgebras, we investigate the construction of Hom-Lie bialgebras as a generalization of Lie bialgebras. In this paper, we mainly show how to construct (triangular coboundary) Hom-Lie bialgebras both through Hom-Lie algebras and Hom-Lie coalgebras. As examples, we consider the construction of (triangular coboundary) Hom-Lie bialgebras on the three-dimensional Heisenberg algebra, on the split simple Lie algebra sl(2) and on E3, the three-dimensional Euclidean space.
Keywords: Hom-Lie algebra, Hom-Lie module, Hom-Lie bialgebra, triangular coboundary Hom-Lie bialgebra.
MSC: 17B99, 17B37, 16W30
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