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

Alexander S. Kleshchev, Joseph W. Loubert, Vanessa Miemietz

Published 2012-10-24Version 1

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 dimension of $R_\al$ is finite, and yields a theory of standard and reduced standard modules for $R_\al$.