Reality-Based Algebras With A Two-Dimensional Representation

Authors

Harvey I. Blau, Northern Illinois University

Author ORCID Identifier

Harvey Blau: https://orcid.org/0000-0002-0020-0016

Publication Title

Linear Algebra and Its Applications

ISSN

243795

Document Type

Article

Abstract

It is shown that a two-dimensional irreducible representation of a reality-based algebra with a standard degree map is determined by the other irreducible representations of the algebra and the action of its given anti-automorphism on the distinguished basis. This generalizes known results for algebras of dimensions 5, 6, 7, and 8. Explicit conclusions equivalent to those for dimensions 5 and 6 are recovered here by specializing the procedure of proof of the main theorem.

First Page

97

Last Page

123

Publication Date

12-30-2019

DOI

10.1016/j.laa.2019.12.034

Keywords

Involution, Irreducible character, Irreducible representation, Matrix units, Orthogonal bases, Reality-based algebra, Row reduction, Unitary matrix

Recommended Citation

Blau, Harvey I., "Reality-Based Algebras With A Two-Dimensional Representation" (2019). NIU Bibliography. 99.
https://huskiecommons.lib.niu.edu/niubib/99

Department

Department of Mathematical Sciences