Poincaré–Birkhoff–Witt bases and Khovanov–Lauda–Rouquier algebras
By Syu Kato. 2012
72 citations recorded by the source corpus.
We generalize Lusztig’s geometric construction of the PBW bases of finite quantum groups of type ADE under the framework of [VaragnoloVasserot, J. reine angew. Math. 659 (2011)]. In particular, every PBW basis of such quantum groups is proven to yield a semi-orthogonal collection in the module category of the KLR-algebras. This enables us to prove Lusztig’s conjecture on the positivity of the canonical (lower global) bases in terms of the (lower) PBW bases. In addition, we verify Kashiwara’s problem on the finiteness of the global dimensions of the KLR-algebras of type ADE.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ffcef57b16c0f222d43711b91fab9da539d41099
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In Algebra and Number Theory
- Alexander S. Kleshchev
- Jonathan Brundan
- Arun Ram
- Aaron D. Lauda
- Mikhail Khovanov
- Raphaël Rouquier
- Weiqiang Wang
- A. Premet
In Geometry and Topology
- Alexander S. Kleshchev
- Jonathan Brundan
- Arun Ram
- Ben Webster
- Aaron D. Lauda
- I. Losev
- Raphaël Rouquier
- C. Stroppel
In Statistical and Nonlinear Physics
Citations in the corpus
- Affine highest weight categories and affine quasihereditary algebras (2014, background): “25, the algebras Rα(C) have finite global dimension, this result was established in [21, 22, 34], see also [5, Appendix].”