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arXiv · 1601.01196

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

Yanqiu Zhou·Yumeng Li·Yunhe Sheng
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Abstract

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.

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BibTeXRIS

Yanqiu Zhou, Yumeng Li, Yunhe Sheng. 2015-12-14. $3$-$Lie_\infty$-algebras and $3$-Lie 2-algebras. https://doi.org/10.1142/s0219498817501705

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