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

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.
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