Mathematica Eterna

Mathematica Eterna
Open Access

ISSN: 1314-3344


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

BAI Ruipu and LIN Lixin

In this paper, we continue to study the structure of four dimensional 3-Lie bialgebras. We discuss the existence of 3-Lie bialgebras of types (Lb, Cd) and (Lb, Ce). It is proved that there do not exist 3-Lie bialgebras of types (Lb1 , Ce), (Lb2 , Ce) and (Lb2 , Cd). There exists only one class of 3-Lie bialgebras of type (Lb, Cd), that is (Lb1 , Cd, ∆1) ( Theorem 3.4 )