Reality-based algebras with a two-dimensional representation

Blau, Harvey I.

doi:10.1016/j.laa.2019.12.034

Linear Algebra and its Applications

2020

DOI: 10.1016/j.laa.2019.12.034

|View full text |Cite

Reality-based algebras with a two-dimensional representation

Harvey I. Blau

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Schur indices for reality-based algebras with two nonreal basis elements

Herman

2020

J. Algebra Appl.

View full text Add to dashboard Cite

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.

show abstract

Schur indices for reality-based algebras with two nonreal basis elements

Herman

2020

J. Algebra Appl.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Reality-based algebras with a two-dimensional representation

Cited by 1 publication

References 8 publications

Schur indices for reality-based algebras with two nonreal basis elements

Schur indices for reality-based algebras with two nonreal basis elements

Contact Info

Product

Resources

About