Crossed modules for Lie 2-algebras

Published 28 Feb 2014 in math.RA, math-ph, and math.MP | (1402.7226v1)

Abstract: The notion of crossed modules for Lie 2-algebras is introduced. We show that, associated to such a crossed module, there is 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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