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15 May 2014 Homological properties of finite-type Khovanov–Lauda–Rouquier algebras
Jonathan Brundan, Alexander Kleshchev, Peter J. McNamara
Duke Math. J. 163(7): 1353-1404 (15 May 2014). DOI: 10.1215/00127094-2681278

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.

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Jonathan Brundan. Alexander Kleshchev. Peter J. McNamara. "Homological properties of finite-type Khovanov–Lauda–Rouquier algebras." Duke Math. J. 163 (7) 1353 - 1404, 15 May 2014. https://doi.org/10.1215/00127094-2681278

Information

Published: 15 May 2014
First available in Project Euclid: 9 May 2014

zbMATH: 1314.16005
MathSciNet: MR3205728
Digital Object Identifier: 10.1215/00127094-2681278

Subjects:
Primary: 16E05, 16S38, 17B37

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 7 • 15 May 2014
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