Mathematica Eterna
Open Access

Abstract

Classification of 3-Lie bialgebras of type (Lb, Cb)

BAI Ruipu and ZHANG Yan

The 4-dimensional 3-Lie coalgebras with one-dimensional derived algebra, and 4-dimensional 3-Lie bialgebras of type (Lb, Cb) are classified. It is proved that there exist two classes 4-dimensional 3-Lie coalgebras with one-dimensional derived algebra which are (L, Cb1 ) and (L, Cb2 ) (Theorem 3.2), and seven classes of 4-dimensional 3-Lie bialgebras of type (Lb, Cb) (Theorem 3.3).