
Journal of Lie Theory 22 (2012), No. 4, 10751089 Copyright Heldermann Verlag 2012 Quasitriangular HomLie Bialgebras Yuanyuan Chen College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China Zhongwei Wang College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China Liangyun Zhang College of Science, Nanjing Agricultural University, Nanjing 210095, P. R. China zlyun@njau.edu.cn Recently certain twisted Lie algebras, socalled HomLie algebras, and their duals have been considered in the literature. In this paper we investigate boundary and quasitriangular HomLie bialgebras further. In particular, we characterize the quasitriangularity of boundary HomLie bialgebras in terms of both a certain HomLie algebra morphism and a certain HomLie coalgebra morphism. We also give a necessary and sufficient condition for a given HomLie algebra and a given 2tensor to admit a coboundary HomLie bialgebra structure. Finally, we generalize the Drinfeld double of a Lie bialgebra to HomLie bialgebras and discuss the dual codouble. Keywords: HomLie algebra, HomLie bialgebra, quasitriangular HomLie bialgebra, (co)double HomLie bialgebra. MSC: 16W30, 17B99, 17B37 [ Fulltextpdf (268 KB)] for subscribers only. 