Reductive homogeneous spaces and nonassociative algebras

TL;DR

This paper surveys Nomizu's classical theorem linking invariant affine connections on reductive homogeneous spaces with nonassociative algebras, providing a comprehensive overview of their relationship.

Contribution

It offers a clear presentation of the theorem and its implications, clarifying the connection between geometric structures and algebraic systems.

Findings

Clarifies the correspondence between invariant affine connections and nonassociative algebras.

Provides a comprehensive overview of Nomizu's theorem.

Highlights the significance of nonassociative algebras in differential geometry.

Abstract

The purpose of these survey notes is to give a presentation of a classical theorem of Nomizu that relates the invariant affine connections on reductive homogeneous spaces and nonassociative algebras.