Noncommutative reality-based algebras of rank 6

Allen Herman, Mikhael Muzychuk, Bangteng Xu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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.

Original languageEnglish
Pages (from-to)90-113
Number of pages24
JournalCommunications in Algebra
Issue number1
StatePublished - 2 Jan 2018
Externally publishedYes


  • Association schemes
  • character tables
  • reality-based algebras
  • table algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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