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Acta Mathematica Vietnamica

A Categorification of the Ribbon Element in Quantum $\mathfrak{sl}(2)$

icon-email Anna Beliakova , Kazuo Habiro

Abstract

We define a bicomplex whose Euler characteristic is the idempotented version of the ribbon element of quantum $\mathfrak{sl}(2)$. We show that properties of this bicomplex descend to the centrality, invertibility, and symmetries of the ribbon element after decategorification.