The recognition problem for table algebras and reality-based algebras

Allen Herman; Mikhail Muzychuk; Bangteng Xu

doi:10.1016/j.jalgebra.2017.01.031

The recognition problem for table algebras and reality-based algebras

Allen Herman, Mikhail Muzychuk, Bangteng Xu

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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⊕M_n(C) for which the RBA has a positive degree map, for all n≥2.

Original language	English
Pages (from-to)	173-191
Number of pages	19
Journal	Journal of Algebra
Volume	479
DOIs	https://doi.org/10.1016/j.jalgebra.2017.01.031
State	Published - 1 Jun 2017
Externally published	Yes

Keywords

C-algebras
Reality-based algebras
Table algebras

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2017.01.031

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title = "The recognition problem for table algebras and reality-based algebras",

abstract = "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.",

keywords = "C-algebras, Reality-based algebras, Table algebras",

author = "Allen Herman and Mikhail Muzychuk and Bangteng Xu",

note = "Funding Information: The author acknowledges the support of the Wilson Endowment of Eastern Kentucky University. Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

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AU - Muzychuk, Mikhail

AU - Xu, Bangteng

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N2 - 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.

AB - 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.

KW - C-algebras

KW - Reality-based algebras

KW - Table algebras

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VL - 479

SP - 173

EP - 191

JO - Journal of Algebra

JF - Journal of Algebra

ER -

The recognition problem for table algebras and reality-based algebras

Abstract

Keywords

ASJC Scopus subject areas

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