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arxiv: 0906.5250 · v2 · pith:QCE3U7XBnew · submitted 2009-06-29 · 🧮 math.DG

Irreducible holonomy algebras of Riemannian supermanifolds

classification 🧮 math.DG
keywords algebrasholonomyirreducibleclassicalriemanniansupermanifoldsassumptionberger
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Possible irreducible holonomy algebras $\g\subset\osp(p,q|2m)$ of Riemannian supermanifolds under the assumption that $\g$ is a direct sum of simple Lie superalgebras of classical type and possibly of a one-dimensional center are classified. This generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.

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