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 | |
【 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.
【 授权许可】
Free
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