The recognition problem for table algebras and reality-based algebras

JOURNAL OF ALGEBRA

卷:479

Article

Herman, Allen¹  Muzychuk, Mikhail²  Xu, Bangteng³ 

[1] Univ Regina, Dept Math & Stat, Regina, SK S4A 0A2, Canada

[2] Netanya Acad Coll, Dept Comp Sci & Math, Univ St 1, IL-42365 Netanya, Israel

[3] Eastern Kentucky Univ, Dept Math & Stat, 521 Lancaster Ave, Richmond, KY 40475 USA

关键词: Table algebras;    C-algebras;    Reality-based algebras;   

DOI  :  10.1016/j.jalgebra.2017.01.031

来源: Elsevier

【 摘 要 】

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 8, we show that there always exists an RBA-basis for which S 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 circle plus M-n(C) for which the RBA has a positive degree map, for all n >= 2. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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