paper

$3$ - $L i e_{\infty}$ -algebras and $3$ -Lie 2-algebras

arXiv:1601.01196 · doi:10.1142/S0219498817501705

Abstract

In this paper, we introduce the notions of a $3$ - $L i e_{\infty}$ -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 $3$ - $L i e_{\infty}$ -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.

16 pages

3-Lie∞​-algebras and 3-Lie 2-algebras

Abstract

$3$ - $L i e_{\infty}$ -algebras and $3$ -Lie 2-algebras