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

Abstract

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