Title: Schur indices for reality-based algebras with two nonreal basis elements
Abstract:This article discusses the representation theory of noncommutative algebras reality-based algebras with positive degree map over their field of definition. When the standard basis contains exactly two...This article discusses the representation theory of noncommutative algebras reality-based algebras with positive degree map over their field of definition. When the standard basis contains exactly two nonreal elements, the main result expresses the noncommutative simple component as a generalized quaternion algebra over its field of definition. The field of real numbers will always be a splitting field for this algebra, but there are noncommutative table algebras of dimension [Formula: see text] with rational field of definition for which it is a division algebra. The approach has other applications, one of which shows noncommutative association scheme of rank [Formula: see text] must have at least three symmetric relations.Read More
Publication Year: 2020
Publication Date: 2020-05-31
Language: en
Type: article
Indexed In: ['crossref']
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