Real fusion rings with degrees 1 and 4

Abstract

Fusion rings are a class of table algebras that generalize group rings with basis the group and character rings of a finite group with basis the irreducible characters. When considering the character ring of a group as a fusion ring, the usual degree of a character coincides with the degree map. Hence classifying fusion rings based on the degree set is a generalization of classifying groups based on the degrees of the irreducible characters. The main theorem classifies real fusion rings with degrees 1 and 4 such that all stabilizers have the same order.

Keywords:

• Finite groups
• fusion rings
• irreducible characters
• table algebras

2010 Mathematics Subject Classification:

• Primary 05E30
• Secondary 16W10
• 20C15
• 16K20

Acknowledgements

The content of this article forms part of the author’s doctoral dissertation [16], which was written under the supervision of Harvey I. Blau and submitted to Northern Illinois University in 2015.

Additional information

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.