A categorification of the square root of -1

Abstract

We give a graphical calculus for a monoidal DG category $\mathcal{I}$ whose Grothendieck group is isomorphic to the ring $\mathbb{Z}[\sqrt{-1}]$. We construct a categorical action of $\mathcal{I}$ which lifts the action of $\mathbb{Z}[\sqrt{-1}]$ on ${\mathbb{Z}}^2$.

11 pages, 4 figures

References in corpus (3)

• An approach to categorification of some small quantum groups II
• An approach to categorification of some small quantum groups
• Hopfological algebra and categorification at a root of unity: the first steps