Representation theory over semifields

TL;DR

This paper explores the classification of group representations over idempotent semifields, focusing on the Boolean semifield, and sets the stage for future work on matroid representations.

Contribution

It introduces a classification framework for torsion group representations over semifields, particularly over the Boolean semifield, and plans to extend this to matroids.

Findings

Classification of torsion group representations over semifields

Special focus on Boolean semifield case

Lays groundwork for matroid representation study

Abstract

We study and classify representations of a torsion group $G$ over an idempotent semifield with special attention on the case over the Boolean semifield $\mathbb{B}$. In subsequent work we extend this theory to studying representations of matroids of low rank.