Irreducible holonomy algebras of Riemannian supermanifolds

Anton S. Galaev

Published 2009-06-29, updated 2013-12-08Version 2

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.