Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents

TL;DR

This paper explicitly constructs a complete set of orthogonal primitive idempotents and matrix units for finite group algebras over nilpotent groups, advancing the understanding of their algebraic structure.

Contribution

It provides an explicit method to find primitive idempotents and matrix units in finite group algebras of nilpotent groups, which was previously not fully characterized.

Findings

Explicit construction of primitive idempotents

Complete set of matrix units in simple components

Enhanced understanding of algebraic structure of group algebras

Abstract

We provide an explicit construction for a complete set of orthogonal primitive idempotents of finite group algebras over nilpotent groups. Furthermore, we give a complete set of matrix units in each simple epimorphic image of a finite group algebra of a nilpotent group.