Holonomy algebras of pseudo-quaternionic-K\"ahlerian manifolds of signature $(4,4)$

TL;DR

This paper classifies the holonomy algebras of pseudo-quaternionic-K"ahlerian manifolds with signature (4,4) and provides a new proof for the classification of their symmetric spaces.

Contribution

It offers a comprehensive classification of holonomy algebras for these manifolds and introduces a novel proof for the symmetric spaces classification.

Findings

Holonomy algebras classified for signature (4,4)

New proof of symmetric spaces classification

Enhanced understanding of geometric structures in pseudo-quaternionic-K"ahlerian manifolds

Abstract

Possible holonomy algebras of pseudo-quaternionic-K\"ahlerian manifolds of signature $(4,4)$ are classified. Using this, a new proof of the classification of simply connected pseudo-quaternionic-K\"ahlerian symmetric spaces of signature $(4,4)$ is obtained.