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.
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