A Minimal left ideal description of Geometric structures in dimensions $6$, $7$, and $8$

TL;DR

This paper explores how minimal left ideals in Clifford algebras can be used to describe and understand special geometric structures in dimensions 6, 7, and 8, providing a new algebraic perspective.

Contribution

It introduces a novel approach linking Clifford algebra ideals with geometric structures in specific dimensions, expanding the algebraic tools for geometric analysis.

Findings

Established correspondence between minimal left ideals and geometric structures in dimensions 6, 7, and 8

Provided algebraic characterizations of geometric features using Clifford algebra ideals

Enhanced understanding of geometric structures through algebraic methods

Abstract

In this paper we relate minimal left ideals on Clifford algebras with special geometric structures in dimensions $6,7,$ and $8$.