Wedderburn decomposition of commutative semisimple group algebras using the Combinatorial Nullstellensatz

TL;DR

This paper provides a geometric approach to decomposing semisimple commutative group algebras over finite abelian groups and finite fields, enhancing understanding of their simple components.

Contribution

It introduces a novel geometric method for Wedderburn decomposition of semisimple commutative group algebras over finite abelian groups and finite fields.

Findings

Explicit description of simple components in the Wedderburn decomposition

Application of combinatorial Nullstellensatz in algebraic decomposition

Extension of results to finite fields

Abstract

In this paper, we present the simple components of the Wedderburn decomposition of semisimple commutative group algebras over finite abelian groups, which we investigate from a geometric point of view. We also present the Wedderburn decomposition of semisimple commutative group algebras over finite fields.