# Inductive algebras for the affine group of a finite field

## TL;DR

This paper investigates the structure of inductive algebras associated with irreducible representations of the affine group over a finite field, revealing their unique maximal and self-adjoint properties.

## Contribution

It establishes the existence and uniqueness of maximal inductive algebras for each irreducible representation of the affine group over a finite field.

## Key findings

- Each irreducible representation has a unique maximal inductive algebra.
- Inductive algebras are self-adjoint.
- The structure of these algebras is characterized for the affine group.

## Abstract

Each irreducible representation of the affine group of a finite field has a unique maximal inductive algebra, and it is self adjoint.