The octonionic projective plane

TL;DR

This paper constructs the octonionic projective plane and discusses its implications for the non-existence of higher-dimensional real division algebras, referencing Adams' solution to the Hopf invariant 1 problem.

Contribution

It provides a construction of the octonionic projective plane and connects it to the proof that higher-dimensional real division algebras do not exist.

Findings

Constructed the octonionic projective plane.

Used the construction to explain the non-existence of higher-dimensional real division algebras.

Referenced Adams' solution to the Hopf invariant 1 problem.

Abstract

This small note, without claim of originality, constructs the projective plane over the octonionic numbers and recalls how this can be used to rule out the existence of higher-dimensional real division algebras, using Adams' solution of the Hopf invariant $1$ problem.