Affine Cellularity of Khovanov-Lauda-Rouquier algebras in type A

We prove that the Khovanov-Lauda-Rouquier algebras $R_{\text{al}}$ of type $A_{\mathrm{\infty }}$ are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_{\text{al}}$ are generated by idempotents. This in particular implies the (known) result that the global dimension of $R_{\text{al}}$ is finite, and yields a theory of standard and reduced standard modules for $R_{\text{al}}$.