Some extension algebras for standard modules over KLR algebras of type A

Khovanov-Lauda-Rouquier algebras Rθ of finite Lie type are affine quasihereditary with standard modules Δ(π) labeled by Kostant partitions of θ. Let Δ be the direct sum of all standard modules. It is known that the Yoneda algebra Eθ:=ExtRθ⁎(Δ,Δ) carries a structure of an A∞-algebra which can be used...

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Bibliographic Details
Published in:Journal of pure and applied algebra 2020-11, Vol.224 (11), p.106410, Article 106410
Main Authors: Buursma, Doeke, Kleshchev, Alexander, Steinberg, David J.
Format: Article
Language:English
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Summary:Khovanov-Lauda-Rouquier algebras Rθ of finite Lie type are affine quasihereditary with standard modules Δ(π) labeled by Kostant partitions of θ. Let Δ be the direct sum of all standard modules. It is known that the Yoneda algebra Eθ:=ExtRθ⁎(Δ,Δ) carries a structure of an A∞-algebra which can be used to reconstruct the category of standardly filtered Rθ-modules. In this paper, we explicitly describe Eθ in two special cases: (1) when θ is a positive root in type A, and (2) when θ is of Lie type A2. In these cases, Eθ turns out to be torsion free and intrinsically formal. We provide an example to show that the A∞-algebra Eθ is non-formal in general.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2020.106410