The recognition problem for table algebras and reality-based algebras

Allen Herman, Mikhail Muzychuk, Bangteng Xu

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Given a finite-dimensional noncommutative semisimple algebra A over C with involution, we show that A always has a basis B for which (A,B) is a reality-based algebra. For algebras that have a one-dimensional representation δ, we show that there always exists an RBA-basis for which δ is a positive degree map. We characterize all RBA-bases of the 5-dimensional noncommutative semisimple algebra for which the algebra has a positive degree map, and give examples of RBA-bases of C⊕Mn(C) for which the RBA has a positive degree map, for all n≥2.

Original languageEnglish
Pages (from-to)173-191
Number of pages19
JournalJournal of Algebra
StatePublished - 1 Jun 2017
Externally publishedYes


  • C-algebras
  • Reality-based algebras
  • Table algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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