How to categorify one-half of quantum gl(1|2)

TL;DR

This paper introduces a new categorification approach for the positive half of the quantum superalgebra gl(1|2) using differential graded rings, advancing the understanding of quantum superalgebra structures.

Contribution

It provides a novel categorification framework for the weight spaces of the positive half of the quantum superalgebra gl(1|2) through differential graded rings.

Findings

Construction of differential graded rings for categorification

Explicit description of weight space categorification

Foundation for further superalgebra categorification studies

Abstract

We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra gl(1|2).