Steenrod Structures on Categorified Quantum Groups

TL;DR

This paper demonstrates how categorified quantum groups can be extended to modules over the Steenrod algebra, linking quantum topology with algebraic topology and providing a new interpretation of the small quantum group.

Contribution

It introduces a natural extension of categorified quantum groups to Steenrod algebra modules, connecting quantum groups with algebraic topology structures.

Findings

Categorified quantum groups can be extended to Steenrod algebra modules

Provides a new interpretation of the small quantum group by Khovanov and Qi

Bridges quantum topology and algebraic topology through this extension

Abstract

Categorified quantum groups play an increasing role in quantum topology and representation theory. The Steenrod algebra is a fundamental component of algebraic topology. In this paper we show that categorified quantum groups can be extended to module categories over the Steenrod algebra in a natural way. This yields an intepretation of the small quantum group by Khovanov and Qi.