We prove that the Khovanov–Lauda–Rouquier algebras Ra of type A8 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 Ra are generated by idempotents. This, in particular, implies the (known) result that the global dimension of Ra is finite, and yields a theory of standard and proper standard modules for Ra.
|Number of pages||21|
|Journal||Journal of the London Mathematical Society|
|Early online date||13 Jun 2013|
|Publication status||Published - 2013|