Explicit idempotents of finite group algebras

TL;DR

This paper derives explicit formulas for primitive idempotents in finite group algebras over finite fields, extending previous results to cyclic groups of prime power order with gcd(q,p)=1.

Contribution

It provides a new explicit expression for primitive idempotents in finite group algebras of cyclic groups of prime power order, generalizing earlier work.

Findings

Explicit formulas for primitive idempotents in finite group algebras.

Extension of previous results to broader class of cyclic groups.

Enhanced understanding of algebraic structure of group algebras.

Abstract

Let $\mathbb F_q$ be a finite field with $q$ elements, $G$ a finite cyclic group of order $p^k$ and $p$ is an odd prime with ${\rm gcd}(q,p)=1$. In this article, we determine an explicit expression for the primitive idempotents of $\mathbb F_qG$. This result extends the result in Arora-Pruthi [1] and Sharma-Bakshi-Dumir-Raka [8].