On 2-Verma modules for quantum $\mathfrak{sl}_2$

Abstract

In this paper we study the superalgebra $A_n$, introduced by the authors in previous work on categorification of Verma modules for quantum $\mathfrak{sl}_2$. The superalgebra $A_n$ is akin to the nilHecke algebra, and shares similar properties. In particular, we prove a uniqueness result about 2-Verma modules on $\Bbbk$-linear 2-categories.