2019/05/01 by Allen Herman, Herman, Allen
Engineering · Mathematics · #16K20 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05E30 Secondary: 16S99 #Rings and Algebras (math.RA) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1905.00445
openalex publication_date 2019/05/01 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
This article discusses the representation theory of noncommutative algebras\nreality-based algebras with positive degree map over their field of definition.\nWhen the standard basis contains exactly two nonreal elements, the main result\nexpresses the noncommutative simple component as a generalized quaternion\nalgebra over its field of definition. The field of real numbers will always be\na splitting field for this algebra, but there are noncommutative table algebras\nof dimension 6 with rational field of definition for which it is a division\nalgebra. The approach has other applications, one of which shows noncommutative\nassociation scheme of rank 7 must have at least three symmetric relations.\n