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arXiv · 1210.6900

Homological properties of finite type Khovanov-Lauda-Rouquier algebras

Jonathan Brundan·Alexander Kleshchev·Peter J. McNamara
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Abstract

We give an algebraic construction of standard modules (infinite dimensional modules categorifying the PBW 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 quasi-hereditary 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. 2012-10-25. Homological properties of finite type Khovanov-Lauda-Rouquier algebras. https://doi.org/10.1215/00127094-2681278

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