Real Clifford algebras and quadratic forms over ${\mathbb F}_2$: two old problems become one

TL;DR

This paper demonstrates that two classical classification theorems, one for quadratic forms over ${ m F}_2$ and one for real Clifford algebras, are fundamentally equivalent, unifying two longstanding mathematical problems.

Contribution

It establishes a deep connection between quadratic forms over ${ m F}_2$ and real Clifford algebras, showing their classifications are essentially the same.

Findings

Proves the equivalence of Dickson's and Chevalley's classification theorems.

Unifies two classical problems in algebra and quadratic form theory.

Provides new insights into the structure of Clifford algebras and quadratic forms.

Abstract

We show equivalence of two old classification theorems: Dickson's classification of quadratic forms over ${\mathbb F}_2$, and Chevalley's classification of real Clifford algebras.