Journal of Lie Theory 15 (2005), No. 1, 125--134
Copyright Heldermann Verlag 2005
Extensions of Super Lie Algebras
Dmitri V. Alekseevsky
Dept. of Mathematics, University of Hull, Cottingham Road, Hull HU6 7RX, England
d.v.alekseevsky@maths.hull.ac.uk
Peter W. Michor
Institut für Mathematik, Universität Wien, Nordbergstr. 15, 1090 Wien, Austria
E.-Schrödinger-Institut für Mathematische Physik, Boltzmanngasse 9, 1090 Wien, Austria
Peter.Michor@esi.ac.at
Wolfgang A. F. Ruppert
Institut für Mathematik, Universität für Bodenkultur, Gregor-Mendel-Str. 33, 1180 Wien, Austria
ruppert@edv1.boku.ac.at
We study (non-abelian) extensions of a super Lie algebra and identify a cohomological obstruction to the existence, parallel to the known one for Lie algebras. An analogy to the setting of covariant exterior derivatives, curvature, and the Bianchi identity in differential geometry is shown.
Keywords: Super Lie algebras, extensions of super Lie algebras, cohomology of super Lie algebras.
MSC: 17B05, 17B56
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