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Extensions of super Lie algebras. (English) Zbl 1098.17014

A super Lie algebra is a 2-graded vector space together with a graded Lie bracket of degree 0. The theory of group extension and their interpretation in terms of cohomology is well known. Analogous results exists e.g., for categories or Lie algebras. This paper study (non-abelian) extensions of a super Lie algebra and identify a cohomological obstruction to the existence. Some analogy with concepts of differential geometry is shown: covariant exterior derivatives, curvature, Bianchi identity.

MSC:

17B55 Homological methods in Lie (super)algebras
17B56 Cohomology of Lie (super)algebras
18G99 Homological algebra in category theory, derived categories and functors

Keywords:

cohomology
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