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

Brundan, Jonathan, Kleshchev, Alexander and McNamara, Peter J. (2014) Homological properties of finite-type Khovanov-Lauda-Rouquier algebras. Duke Mathematical Journal, 163 7: 1353-1404. doi:10.1215/00127094-2681278

Author Brundan, Jonathan
Kleshchev, Alexander
McNamara, Peter J.
Title Homological properties of finite-type Khovanov-Lauda-Rouquier algebras
Journal name Duke Mathematical Journal   Check publisher's open access policy
ISSN 0012-7094
Publication date 2014
Year available 2014
Sub-type Article (original research)
DOI 10.1215/00127094-2681278
Open Access Status
Volume 163
Issue 7
Start page 1353
End page 1404
Total pages 52
Place of publication Durham, NC United States
Publisher Duke University Press
Collection year 2015
Language eng
Abstract 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.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 5 times in Thomson Reuters Web of Science Article | Citations
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Created: Fri, 17 Apr 2015, 15:44:48 EST by Kay Mackie on behalf of School of Mathematics & Physics