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3-Lie∞-algebras and 3-Lie 2-algebras
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In this paper, we introduce the notions of a [Formula: see text]-[Formula: see text]-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 [Formula: see text]-[Formula: see text]-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.
World Scientific Pub Co Pte Lt
Title: 3-Lie∞-algebras and 3-Lie 2-algebras
Description:
In this paper, we introduce the notions of a [Formula: see text]-[Formula: see text]-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 [Formula: see text]-[Formula: see text]-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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