Journal of Lie Theory 18 (2008), No. 2, 413--432
Copyright Heldermann Verlag 2008
Non-Abelian Cohomology and Extensions of Lie Algebras
Nikoloz Inassaridze
National Center for Science and Technology, A. Razmadze Mathematical Institute, M. Alexidze St. 1, Tbilisi 0193, Georgia
and: Dpto. Matemática Aplicada I, Universidad de Vigo, EUIT Forestal, 36005 Pontevedra, Spain
niko.inas@gmail.com
Emzar Khmaladze
National Center for Science and Technology, A. Razmadze Mathematical Institute, M. Alexidze St. 1, Tbilisi 0193, Georgia
khmal@rmi.acnet.ge
Manuel Ladra
Departamento de Algebra, Universidad de Santiago, 15782 Santiago, Spain
ladra@usc.es
We introduce the second non-abelian cohomology of Lie algebras with coefficients in crossed modules using the generalised notion of Lie algebra of derivations, and establish a relationship of this cohomology with Lie algebra extensions by crossed modules. We extend the seven-term exact non-abelian cohomology sequence of Guin to a nine-term exact sequence.
Keywords: Derivations, crossed modules, non-abelian cohomology, extensions of Lie algebras.
MSC: 17B40, 17B56, 18G10, 18G50
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