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Irreducible holonomy algebras of Riemannian supermanifolds
Authors:Anton S. Galaev
Affiliation:1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University in Brno, Kotl???sk?? 2, 611 37, Brno, Czech Republic
Abstract:Possible irreducible holonomy algebras mathfrakg ì mathfrakosp(p, q|2m){mathfrak{g}subsetmathfrak{osp}(p, q|2m)} of Riemannian supermanifolds under the assumption that mathfrakg{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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