| Institution: | 1.Department of Mathematics,Xinyang Normal University,Henan,China;2.Laboratoire de Mathématiques, Informatique et Applications,University of Haute Alsace,Mulhouse,France;3.Department of Mathematics,Jilin University,Changchun,China |
| Abstract: | In this paper, we introduce the notion of generalized representation of a 3-Lie algebra, by which we obtain a generalized semidirect product 3-Lie algebra. Moreover, we develop the corresponding cohomology theory. Various examples of generalized representations of 3-Lie algebras and computation of 2-cocycles of the new cohomology are provided. Also, we show that a split abelian extension of a 3-Lie algebra is isomorphic to a generalized semidirect product 3-Lie algebra. Furthermore, we describe general abelian extensions of 3-Lie algebras using Maurer-Cartan elements. |
