The quaternion group has ghost number three

TL;DR

This paper proves that the group algebra of the quaternion group over any field of characteristic two has a ghost number of three, revealing a specific algebraic property related to its structure.

Contribution

The paper establishes that the ghost number of the quaternion group's algebra over characteristic two fields is exactly three, a new result in algebraic representation theory.

Findings

Ghost number of quaternion group algebra is three

Valid over any field of characteristic two

Advances understanding of algebraic properties of group algebras

Abstract

We prove that the group algebra of the quaternion group $Q_8$ over any field of characteristic two has ghost number three.