Abstract
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.
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