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On Lie algebra crossed modules

Friedrich Wagemann
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Abstract

This article constructs a crossed module corresponding to the generator of the third cohomology group with trivial coefficients of a complex simple Lie algebra. This generator reads as <[,],>, constructed from the Lie bracket [,] and the Killing form <,>. The construction is inspired by the corresponding construction for the Lie algebra of formal vector fields in one formal variable on R, and its subalgebra sl_2(R), where the generator is usually called Godbillon-Vey class.

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Friedrich Wagemann. 2006-11-13. On Lie algebra crossed modules. https://arxiv.org/abs/math/0611375

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