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Tambara-Yamagami Categories over the Reals: The Non-Split Case

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arxiv 2303.17843 v3 pith:X3YR5UIR submitted 2023-03-31 math.QA math.CT

Julia Plavnik , Sean Sanford , Dalton Sconce This is my paper · ORCID
classification math.QAmath.CT
keywords rulessimplefusionobjectsrealtambarayamagamiassociator
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Tambara and Yamagami investigated a simple set of fusion rules with only one non-invertible object, and proved under which circumstances those rules could be given a coherent associator. We consider a generalization of such fusion rules to the setting where simple objects are no longer required to be split simple. Over the real numbers, this means that objects are either real, complex, or quaternionic. In this context, we prove a similar categorification result to the one of Tambara and Yamagami.

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