Affine cellularity of Khovanov-Lauda-Rouquier algebras in type <i>A</i>
Affine cellularity of Khovanov-Lauda-Rouquier algebras in type <i>A</i>
We prove that the Khovanov-Lauda-Rouquier algebras $R_\al$ of type $A_\infty$ 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 $R_\al$ are generated by idempotents. This in particular implies the (known) result that the global …