DG-Enhanced Hecke and KLR Algebras

Abstract

We construct DG-enhanced versions of the degenerate affine Hecke algebra and of the affine Hecke algebra. We extend Brundan-Kleshchev and Rouquier's isomorphism and prove that after completion DG-enhanced versions of affine Hecke algebras (degenerate or nondegenerate) are isomorphic to completed DG-enhanced versions of KLR algebras for suitably defined quivers. As a byproduct, we deduce that these DG-algebras have homologies concentrated in degree zero. These homologies are isomorphic respectively to the degenerate cyclotomic Hecke algebra and the cyclotomic Hecke algebra.

References in corpus (10)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Graded decomposition numbers for cyclotomic Hecke algebras
• Knot invariants and higher representation theory
• On graded presentations of Hecke algebras and their generalizations
• An approach to categorification of Verma modules
• Cyclotomic Yokonuma-Hecke algebras are cyclotomic quiver Hecke algebras
• Affine Hecke algebras and generalisations of quiver Hecke algebras for type B
• Affine quiver Schur algebras and $p$-adic $G{L}_n$
• On 2-Verma modules for quantum ${\mathfrak{sl}}_2$

Cited by in corpus (1)

• Handlebody diagram algebras