Affine Cellularity of Khovanov-Lauda-Rouquier Algebras of Finite Types

Abstract

We prove that the Khovanov-Lauda-Rouquier algebras $R_{\alpha }$ of finite type 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 $R_{\alpha }$ are generated by idempotents. This in particular implies the (known) result that the global dimension of $R_{\alpha }$ is finite.