Mathematica Eterna
Open Access

Abstract

3-Lie bialgebras (Lc , Cd) and (Lc , Ce)

BAI Ruipu and GUO Weiwei

In this paper, we discuss the structure of four dimensional 3-Lie bialgebras of type (Lci , Cd) and (Lci , Ce) for i = 1, 2, 3. It is proved that there do not exist 3-Lie bialgebras of types (Lci , Cd) and (Lci , Ce) for i = 1, 2 (Theorem 3.2), and there exist only three classes of 3-Lie bialgebras of types (Lc3 , Cd) (Theorem 3,3), and two classes of 3-Lie bialgebras of types (Lc3 , Ce) (Theorem 3.4).