Some Results on Non-Hermitian Ribbon Fusion Categories
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Several open problems have been asked and are being solved on the nature of dagger structures that can be defined on Fusion Categories, and many results have been shown for Hermitian (positive dagger) Fusion Categories. However, Non-Hermitian Fusion Categories do exist, the most prominent example of them being the Yang-Lee Category. Using properties of Fusion Categories, previous results that has been found about Fusion Categories with a Hermitian Dagger Structure, and properties that arise from the existence of a Ribbon Structure and the ability to define a braiding, we now shift our focus on investigating Ribbon Fusion Categories that have a Non-Hermitian Dagger structure on them. Utilizing the rich and complicated structure of these categories, we discuss the outline of proofs of theorems on the Muger center, braiding, and spherical structure of such a fusion category, and discuss a potential construction of a TQFT using these results. slides