Crossed modules for Lie 2-algebras
classification
🧮 math.RA
math-phmath.MP
keywords
crossedalgebrasmodulesalgebrastrictstructureassociatedclassify
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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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