Primitive Central idempotents and the Wedderburn Decomposition of a Rational Abelian Group Algebra

TL;DR

This paper provides an explicit method to identify primitive central idempotents and determine the Wedderburn decomposition of rational group algebras for finite abelian groups.

Contribution

It introduces a new explicit approach using long presentations to analyze the structure of rational group algebras of finite abelian groups.

Findings

Explicit description of primitive central idempotents

Determination of Wedderburn decompositions

Application to rational group algebras of finite abelian groups

Abstract

In this paper we give an explicit description of primitive central idempotents of rational group algebras of finite abelian groups using long presentation, and determine their Wedderburn decompositions.