On Noncommutative Integral Standard Generalized Table Algebras of Dimension 6

Abstract

We will investigate the structure of noncommutative imprimitive association schemes of rank 6 and the representation of their adjacency algebras. From this investigation, we will construct new integral standard generalized table algebras with three parameters. These algebras are noncommutative, imprimitive, and 6-dimensional.

Key Words:

• Association schemes
• Conference graphs
• Integral standard generalized table algebras
• Noncommutative

2010 Mathematics Subject Classification:

• 05E30
• 16W99

ACKNOWLEDGMENT

The author thanks the anonymous referees for their carefully reading the article and giving valuable comments. He also thanks A. Hanaki for valuable suggestions and comments.

Notes

Communicated by A. Turull.