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Crossed Modules for Lie 2-Algebras

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Abstract

We define the notion of crossed modules for Lie 2-algebras. To a given crossed module, we associate a strict Lie 3-algebra structure on its mapping cone complex and a strict Lie 2-algebra structure on its derivations. Finally, we classify strong crossed modules by means of the third cohomology group of Lie 2-algebras.

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Authors and Affiliations

  1. Department of Mathematics and LMAM, Peking University, Beijing, 100871, China

    Honglei Lang & Zhangju Liu

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  1. Honglei Lang
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  2. Zhangju Liu
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Correspondence to Honglei Lang.

Additional information

The first author is supported by NSFC 11471179 and China Scholarship Council and the second author is supported by NSFC 11471139.

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Lang, H., Liu, Z. Crossed Modules for Lie 2-Algebras. Appl Categor Struct 24, 53–78 (2016). https://doi.org/10.1007/s10485-015-9389-8

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  • DOI: https://doi.org/10.1007/s10485-015-9389-8

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