EKU Faculty and Staff Scholarship
 

Department

Mathematics and Statistics

Document Type

Article

Publication Date

1-2018

Abstract

We show that noncommutative standard reality-based algebras (RBAs) of dimension 6 are determined up to exact isomorphism by their character tables. We show that the possible character tables of these RBAs are determined by seven real numbers, the first four of which are positive and the remaining three real numbers can be arbitrarily chosen up to a single exception. We show how to obtain a concrete matrix realization of the elements of the RBA-basis from the character table. Using a computer implementation, we give a list of all noncommutative integral table algebras of rank 6 with orders up to 150. Four in the list are primitive, but we show three of them cannot be realized as adjacency algebras of association schemes. In the last section of the paper, we apply our methods to give a precise description of the noncommutative integral table algebras of rank 6 for which the multiplicity of both linear characters is 1.

Journal Title

Communications in Algebra

Journal Volume

46

Journal Issue

1

Article Starting Page

90

Article Ending Page

113

Included in

Algebra Commons

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