Primitive Central Idempotents of Rational Group Algebras

TL;DR

This paper provides a detailed description of primitive central idempotents in rational group algebras, addressing previous gaps involving unknown scalars and answering existing questions in the field.

Contribution

It offers a refined description of primitive central idempotents in rational group algebras, resolving issues related to unknown scalars from prior research.

Findings

Clarified the structure of primitive central idempotents

Resolved previous uncertainties involving scalar values

Enhanced understanding of rational group algebra decomposition

Abstract

We give a description of the primitive central idempotents of the rational group algebra QG of a finite group G. Such a description is already investigated by Jespers, Olteanu and del R\'io, but some unknown scalars are involved. Our description also gives answers to their questions.