A categorification of the ribbon element in quantum sl(2)

TL;DR

This paper constructs a bicomplex model for the ribbon element in quantum sl(2), revealing its algebraic properties through categorification and connecting these to known quantum invariants.

Contribution

It introduces a bicomplex whose Euler characteristic categorifies the ribbon element, elucidating its properties via a new algebraic framework.

Findings

The bicomplex's Euler characteristic equals the idempotented ribbon element.

Properties like centrality and invertibility are shown to descend from the bicomplex.

The work bridges categorification with quantum group invariants.

Abstract

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