Quinn Kolt
University of California, Santa Barbara
Title
Formal ribbon extensions of quasitriangular Hopf algebras
Abstract
Reshetikhin and Turaev (1990) introduced the notion of a ribbon Hopf algebra and showed that every quasitriangular Hopf algebra can be extended to a ribbon Hopf algebra by formally adjoining a ribbon element. We study the representation theory of these formal ribbon extensions by expressing it in terms of the representation tneory of the original algebra. To prove our main result, we apply some techniques from operator algebra and model theory. We also show that, in the semisimple case, the formal ribbon extension agrees with pivotalization of the representation category, as introduced by Etingof, Nikshych, and Ostrik (2005).
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