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.
Acknowledgements
The authors would like to thank Professor Chengming Bai for many valuable suggestions.
Notes
No potential conflict of interest was reported by the authors.