Structure of Finite dihedral group algebra

TL;DR

This paper explores the relationship between the irreducible idempotents of cyclic group algebras and dihedral group algebras over finite fields, revealing structural connections under certain conditions.

Contribution

It establishes a link between the irreducible idempotents of cyclic and dihedral group algebras over finite fields when gcd(q,n)=1.

Findings

Relation between irreducible idempotents of cyclic and dihedral group algebras

Structural insights into group algebra decomposition over finite fields

Conditions for the correspondence when gcd(q,n)=1

Abstract

In this article, we show the relation between the irreducible idempotents of the cyclic group algebra $\mathbb F_qC_n$ and the central irreducible idempotents of the group algebras $\mathbb F_qD_{2n}$, where $\mathbb F_q$ is a finite field with $q$ elements and $D_{2n}$ is the dihedral group of order $2n$, where ${\rm gcd}(q,n)=1$.