Irreducible complex skew-Berger algebras

Abstract

Irreducible skew-Berger algebras $\g\subset\gl(n,\Co)$, i.e. algebras spanned by the images of the linear maps $R:\odot^2\Co^n\to\g$ satisfying the Bianchi identity, are classified. These Lie algebras can be interpreted as irreducible complex Berger superalgebras contained in $\gl(0|n,\Co)$.

23 pages

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• Prolongations of Lie algebras and applications
• The spaces of curvature tensors for holonomy algebras of Lorentzian manifolds
• Recent Advances in the Theory of Holonomy
• The analogs of Riemann and Penrose tensors on supermanifolds
• Holonomy of supermanifolds

Cited by in corpus (6)

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• Classification of maximal transitive prolongations of super-Poincaré algebras
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• Irreducible holonomy algebras of odd Riemannian supermanifolds