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- Title
3--algebras and 3-Lie 2-algebras.
- Authors
Zhou, Yanqiu; Li, Yumeng; Sheng, Yunhe
- Abstract
In this paper, we introduce the notions of a --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 --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.
- Subjects
LIE algebras; SYMPLECTIC geometry; HOMOTOPY theory; MATHEMATICAL analysis; MATHEMATICAL proofs
- Publication
Journal of Algebra & Its Applications, 2017, Vol 16, Issue 9, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498817501717