Homological properties of finite type Khovanov-Lauda-Rouquier algebras

By Jonathan Brundan, Alexander S. Kleshchev, Peter J. McNamara. 2012

82 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f64f6f9c4b0d1ecbc048188643617f7caeaf5123

How researchers see this paper

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In Computational Theory and Mathematics

1. Alexander S. Kleshchev
2. Ben Webster
3. I. Losev

In Geometry and Topology

1. Alexander S. Kleshchev
2. Jonathan Brundan
3. Arun Ram
4. Ben Webster
5. Aaron D. Lauda
6. I. Losev
7. Raphaël Rouquier
8. C. Stroppel

In Mathematical Physics

1. Alexander S. Kleshchev
2. Jonathan Brundan
3. Aaron D. Lauda
4. Raphaël Rouquier
5. Mikhail Khovanov
6. I. Losev
7. Arun Ram
8. Weiqiang Wang

Citations in the corpus

• Affine highest weight categories and affine quasihereditary algebras (2014, methodology): “It is proved in [5] using homological and representation theoretic methods that Rα(C)-mod is a polynomial highest”