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

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
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