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

Abstract

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 $R_\al$.

References in corpus (3)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• PBW bases and KLR algebras

Cited by in corpus (11)

• Affine highest weight categories and affine quasihereditary algebras
• The many graded cellular bases of Hecke algebras
• On the structure of cyclotomic nilHecke algebras
• Cellularity and subdivision of KLR and weighted KLRW algebras
• Homomorphisms between standard modules over finite type KLR algebras
• On 2-Verma modules for quantum ${\mathfrak{sl}}_2$
• Ring theoretical properties of affine cellular algebras
• Schubert Class and cyclotomic nilHecke algebras
• Cellularity of KLR and weighted KLRW algebras via crystals
• Strands algebras and the affine highest weight property for equivariant hypertoric categories
• Affine quasi-heredity of affine Schur algebras