Irreducible holonomy algebras of odd Riemannian supermanifolds

Abstract

Possible irreducible holonomy algebras $\g\subset\sp(2m,\Real)$ of odd Riemannian supermanifolds and irreducible subalgebras $\g\subset\gl(n,\Real)$ with non-trivial first skew-symmetric prolongations are classified. An approach to the classification of some classes of the holonomy algebras of Riemannian supermanifolds is discussed.