标题： $3$-$Lie_\infty$-代数和$3$-李2-代数 显示英文标题

标题： $3$-$Lie_\infty$-algebras and $3$-Lie 2-algebras

摘要： 本文中，我们引入了 $3$-$Lie_\infty$-代数和3-Lie 2-代数的概念。 前者是满足基本恒等式的3-Lie代数的模型，后者是3-Lie代数的范畴化。 我们证明了2项 $3$-$Lie_\infty$-代数的2-范畴与3-Lie 2-代数的2-范畴是等价的。 详细研究了骨骼化和严格3-Lie 2-代数。 给出了由辛3-Lie代数构造3-Lie 2-代数的方法。 显示英文摘要

摘要： In this paper, we introduce the notions of a $3$-$Lie_\infty$-algebra and a 3-Lie 2-algebra. The former is a model for a 3-Lie algebra that satisfy the fundamental identity up to all higher homotopies, and the latter is the categorification of a 3-Lie algebra. We prove that the 2-category of 2-term $3$-$Lie_\infty$-algebras is equivalent to the 2-category of 3-Lie 2-algebras. Skeletal and strict 3-Lie 2-algebras are studied in detail. A construction of a 3-Lie 2-algebra from a symplectic 3-Lie algebra is given.