# Resolutions of standard modules over KLR algebras of type $A$

## TL;DR

This paper constructs explicit projective resolutions of standard modules over Khovanov-Lauda-Rouquier algebras of type A, advancing understanding of their homological properties in finite Lie types.

## Contribution

It provides explicit projective resolutions of standard modules in type A KLR algebras, a novel contribution to the homological study of these algebras.

## Key findings

- Explicit projective resolutions constructed for standard modules
- Enhanced understanding of homological properties of KLR algebras in type A
- Supports further algebraic and categorical investigations

## Abstract

Khovanov-Lauda-Rouquier algebras $R_\theta$ of finite Lie type are affine quasihereditary with standard modules $\Delta(\pi)$ labeled by Kostant partitions $\pi$ of $\theta$. In type $A$, we construct explicit projective resolutions of standard modules $\Delta(\pi)$.