Actions of \(\mathfrak{sl}_2\) on algebras appearing in categorification (Q6150023)

Summary: We prove that many of the recently-constructed algebras and categories which appear in categorification can be equipped with an action of \(\mathfrak{sl}_2\) by derivations. The \(\mathfrak{sl}_2\) representations which appear are filtered by tensor products of coVerma modules. In a future paper, we will address the implications of the \(\mathfrak{sl}_2\) structure for categorification.