Burnside-Brauer Theorem and Character Products in Table Algebras

TL;DR

This paper extends classical character theory to table algebras, establishing a Burnside-Brauer type theorem and exploring character products, thus broadening the algebraic framework for analyzing symmetries.

Contribution

It introduces character products for table algebras and proves a Burnside-Brauer theorem analogue, linking quotient and original algebra characters.

Findings

Irreducible characters of quotient table algebras correspond to those of the original.

Conditions identified for when character products are characters.

Established a Burnside-Brauer theorem for finite group table algebras.

Abstract

In this paper, we first show that the irreducible characters of a quotient table algebra modulo a normal closed subset can be viewed as the irreducible characters of the table algebra itself. Furthermore, we define the character products for table algebras and give a condition in which the products of two characters are characters. Thereafter, as a main result we state and prove the Burnside-Brauer Theorem on finite groups for table algebras.