Irreducible holonomy algebras of odd Riemannian supermanifolds

TL;DR

This paper classifies irreducible holonomy algebras of odd Riemannian supermanifolds and explores their structure, providing a foundation for understanding the geometric properties of these supermanifolds.

Contribution

It introduces a classification of irreducible holonomy algebras for odd Riemannian supermanifolds and analyzes subalgebras with non-trivial first skew-symmetric prolongations.

Findings

Classification of possible irreducible holonomy algebras in the super setting

Identification of subalgebras with specific prolongation properties

Discussion of approaches to classify holonomy algebras in 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.