Hom-Lie 2-algebras

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• 作者：Yunhe Sheng ; ^{shengyh@jlu.edu.cn} ; Danhua Chen
• 关键词：17B99 ; 55U15
• 刊名：Journal of Algebra
• 出版年：2013
• 出版时间：15 February, 2013
• 年：2013
• 卷：376
• 期：Complete
• 页码：174-195
• 全文大小：289 K

文摘

In this paper, we introduce the notions of hom-Lie 2-algebras, which is the categorification of hom-Lie algebras, -algebras, which is the hom-analogue of -algebras, and crossed modules of hom-Lie algebras. We prove that the category of hom-Lie 2-algebras and the category of 2-term -algebras are equivalent. We give a detailed study on skeletal hom-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 hom-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.