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Irreducible holonomy algebras of Riemannian supermanifolds

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Abstract

Possible irreducible holonomy algebras \({\mathfrak{g}\subset\mathfrak{osp}(p, q|2m)}\) of Riemannian supermanifolds under the assumption that \({\mathfrak{g}}\) is a direct sum of simple Lie superalgebras of classical type and possibly of a 1-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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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University in Brno, Kotlářská 2, 611 37, Brno, Czech Republic

    Anton S. Galaev

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  1. Anton S. Galaev
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Correspondence to Anton S. Galaev.

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Communicated by N. Hitchin (Oxford).

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Galaev, A.S. Irreducible holonomy algebras of Riemannian supermanifolds. Ann Glob Anal Geom 42, 1–27 (2012). https://doi.org/10.1007/s10455-011-9299-4

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