On Morita Equivalences Between KLR Algebras and VV Algebras

TL;DR

This paper investigates the properties of VV algebras, establishing Morita equivalences with KLR algebras, and uses these to prove properties like affine cellularity and quasi-heredity of VV algebras.

Contribution

It introduces Morita equivalences between KLR and VV algebras, enabling new insights into VV algebra properties.

Findings

Established Morita equivalences between KLR and VV algebras

Proved VV algebras are affine cellular and affine quasi-hereditary

Enhanced understanding of VV algebra module categories

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.