N-Lie bialgebras. Issue 2 (1st February 2018) - Bai, Ruipu; Guo, Weiwei; Lin, Lixin; Zhang, Yan
Abstract: We define n -Lie coalgebras with rank r and discuss their structures. We also introduce n -Lie bialgebras and investigate their structures. A triple is an n -Lie bialgebra if and only if is a conformal 1-cocycle on the n -Lie algebra L associated to L -modules, . Furthermore we study two-dimensional extensions of finite dimensional n -Lie bialgebras, and construct an -dimensional -Lie bialgebra associated to an m dimensional n -Lie bialgebra . Finally we discuss the bialgebra structure on the finite dimensional simple n -Lie algebra, and prove that the only bialgebra structures on the simple n -Lie algebra are of rank zero and rank two.