Reality-Based Algebras With A Two-Dimensional Representation
Author ORCID Identifier
Harvey Blau: https://orcid.org/0000-0002-0020-0016
Linear Algebra and Its Applications
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.
Involution, Irreducible character, Irreducible representation, Matrix units, Orthogonal bases, Reality-based algebra, Row reduction, Unitary matrix
Blau, Harvey I., "Reality-Based Algebras With A Two-Dimensional Representation" (2019). NIU Bibliography. 99.
Department of Mathematical Sciences