On the classification of the real vector subspaces of a quaternionic vector space

TL;DR

This paper classifies real vector subspaces within quaternionic vector spaces using a covariant functor that links pairs of spaces to coherent sheaves over the sphere, providing a structured understanding of their relationships.

Contribution

It introduces a novel classification method for real subspaces of quaternionic vector spaces via a covariant functor and coherent sheaves, advancing the theoretical framework.

Findings

Complete classification of real subspaces in quaternionic vector spaces

Introduction of a covariant functor linking spaces to sheaves

Establishment of a correspondence between subspaces and sheaves

Abstract

We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which, to any pair formed of a quaternionic vector space and a real subspace, associates a coherent sheaf over the sphere.