期刊论文详细信息
JOURNAL OF ALGEBRA 卷:376
Hom-Lie 2-algebras
Article
Sheng, Yunhe1  Chen, Danhua1 
[1] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China
关键词: Hom-Lie algebras;    Quadratic ham-Lie algebras;    Ham-Lie 2-algebras;    HL infinity-algebras;    Crossed module of ham-Lie algebras;    Hom-left-symmetric algebras;    Symplectic hom-Lie algebras;   
DOI  :  10.1016/j.jalgebra.2012.11.032
来源: Elsevier
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【 摘 要 】

In this paper, we introduce the notions of hom-Lie 2-algebras, which is the categorification of ham-Lie algebras, HL infinity-algebras, which is. the hom-analogue of L-infinity-algebras; and crossed modules of hom-Lie algebras. We prove that the category of hom-Lie 2-algebras and the category of 2-term HL infinity-algebras are equivalent. We give a detailed study on skeletal ham-Lie 2-algebras. In particular, we construct the hom-analogues of the string Lie 2-algebras associated to any semisimple involutive hom-Lie algebras. We also proved that there is a one-to-one correspondence between strict. ham-Lie 2-algebras and crossed modules of hom-Lie algebras. We give the construction of strict hom-Lie 2-algebras from hom-left-symmetric algebras and symplectic hom-Lie algebras. (c) 2012 Elsevier Inc. All rights reserved.

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