The recognition problem for table algebras and reality-based algebras

2015/06/17 by Allen Herman, Herman, Allen, Mikhael Muzychuk +3
Engineering · Mathematics · #05E30 #20C15 #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1506.05476

openalex publication_date 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite-dimensional noncommutative semisimple algebra A with involution, we show that A always has an RBA-basis. We look for an RBA-basis that has integral or rational structure constants, and ask if the RBA admits a positive degree map. For RBAs that have a positive degree map, we try to find an RBA-basis with nonnegative structure constants to determine if there is a generalized table algebra structure. We settle these questions for the algebras ℂ ⊕ M_n(ℂ), n ≥ 2.

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