Non abelian cohomology of extensions of Lie algebras as Deligne groupoid

2013/10/02 by Fregier, Yael · 1 citation
#18G50 #20J06 #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1310.0959

Abstract

In this note we show that the theory of non abelian extensions of a Lie algebra \mathfrakg by a Lie algebra \mathfrakh can be understood in terms of a differential graded Lie algebra L. More precisely we show that the non-abelian cohomology H²_nab(\mathfrakg,\mathfrakh) is MC(L), the π₀ of the Deligne groupoid of L.

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