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Bialgebra structures on 3-Lie algebra Ld

BAI Ruipu and Lin Lixin

In this paper, we discuss bialgebra structures on the 3-Lie algebra Ld. It is proved that there do not exist 3-Lie bialgebras of types (Ld, Cb2 ), (Ld, Cc1 ), (Ld, Cc2 ), (Ld, Cd) and (Ld, Ce), and there exist only five classes of 3-Lie bialgebras of types on Ld which are (Ld, 0), (Ld, Cb1 , ∆1), (Ld, Cb1 , ∆2), (Ld, Cc3 , ∆1) and (Ld, Cc3 , ∆2).