Homological properties of finite-type Khovanov–Lauda–Rouquier algebras

Homological properties of finite-type Khovanov–Lauda–Rouquier algebras

We give an algebraic construction of standard modules—infinite-dimensional modules categorifying the Poincaré–Birkhoff–Witt basis of the underlying quantized enveloping algebra—for Khovanov–Lauda–Rouquier algebras in all finite types. This allows us to prove in an elementary way that these algebras...

Full description

Saved in:
Bibliographic Details
Published in:Duke mathematical journal Vol. 163; no. 7; pp. 1353 - 1404
Main Authors: Brundan, Jonathan, Kleshchev, Alexander, McNamara, Peter J.
Format: Journal Article
Language:English
Published: Duke University Press 15-05-2014
Subjects:
16E05
16S38
17B37
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We give an algebraic construction of standard modules—infinite-dimensional modules categorifying the Poincaré–Birkhoff–Witt basis of the underlying quantized enveloping algebra—for Khovanov–Lauda–Rouquier algebras in all finite types. This allows us to prove in an elementary way that these algebras satisfy the homological properties of an “affine quasihereditary algebra.” In simply laced types these properties were established originally by Kato via a geometric approach. We also construct some Koszul-like projective resolutions of standard modules corresponding to multiplicity-free positive roots.
ISSN:0012-7094
1547-7398
DOI:10.1215/00127094-2681278