On Morita Equivalences Between KLR Algebras and VV Algebras

Abstract

This paper is investigative work into the properties of a family of graded algebras recently defined by Varagnolo and Vasserot, which we call VV algebras. We compare categories of modules over KLR algebras with categories of modules over VV algebras, establishing various Morita equivalences. Using these Morita equivalences we are able to prove several properties of certain classes of VV algebras such as (graded) affine cellularity and affine quasi-heredity.