Homological properties of finite-type Khovanov-Lauda-Rouquier algebras. (English) Zbl 1314.16005

Brundan, Jonathan; Kleshchev, Alexander; McNamara, Peter J.

Duke Math. J. 163, No. 7, 1353-1404 (2014).

The paper under review studies Khovanov-Lauda-Rouquier (KLR) algebras of finite type. The authors propose an algebraic construction of standard modules for these algebras. These standard modules correspond to a PBW basis of the quantized enveloping algebra when the latter is categorified by using KLR algebras. The paper establishes, in an algebraic way, various homological properties of these modules motivated by the theory of stratified algebras. For some standard modules the authors construct Koszul-like projective resolutions.

Reviewer: Volodymyr Mazorchuk (Uppsala)

MSC:

16E05	Syzygies, resolutions, complexes in associative algebras
17B37	Quantum groups (quantized enveloping algebras) and related deformations
20C08	Hecke algebras and their representations
05E10	Combinatorial aspects of representation theory

Keywords:

Khovanov-Lauda-Rouquier algebras; KLR algebras; standard modules; quantized enveloping algebras; stratified algebras; projective resolutions

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