An approach to categorification of some small quantum groups

TL;DR

This paper presents a categorification of a portion of the small quantum sl(2) at a prime root of unity, with a proposed extension to more general simply-laced cases, advancing the understanding of quantum group structures.

Contribution

It introduces a categorification method for small quantum sl(2) at roots of unity and suggests a broader extension to simply-laced quantum groups.

Findings

Successful categorification of half of small quantum sl(2)

Proposed extension to arbitrary simply-laced cases

Framework for future generalizations

Abstract

We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.