N-Lie bialgebras. Issue 2 (1st February 2018)

• Record Type: Journal Article
• Authors: Bai, Ruipu; Guo, Weiwei; Lin, Lixin; Zhang, Yan
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 2(2018)
• Page Start: 382
• Page End: 397
• Publication Date: 2018-02-01
• Subjects: n-Lie algebra -- n-Lie bialgebra -- n-Lie coalgebra -- two-dimensional extension; 17B05 -- 17D99; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1299090
• Languages: English
• ISSNs: 0308-1087

Abstract

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.