L_∞-代数的等价定义

An Equivalent Definition of L_∞-Algebras

L_∞-代数是李代数的推广,近年来受到了很多学者的关注.利用大括号给出了L_∞-代数的等价定义,这个等价定义的形式相比之前更加简单.在此基础上,类比李2-双代数的研究,给出了L_∞-余代数和L_∞-双代数的合理定义,这对于L_∞-代数的研究起到了一些促进作用.

L ＂-algebras are sort of generalizations of Lie algebras,which has attracted many scholars＇ attention in recent years. In this paper,an equivalent definition of L_∞-algebras is introduced via the big bracket,The form of this equivalence definition is simpler than before.Based on this,an analogy study of lie 2-algebras is conducted,and the definition of L ＂-coalgebras and L_∞-bialgebras are given. All of above have played a catalytic role in the study of algebra.