Explicit computation of the A_∞-algebra E_θ for KLR algebras when θ is a positive root in type A or of type A2 shows it is torsion-free and intrinsically formal, with a general example of non-formality.
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Some extension algebras for standard modules over KLR algebras of type $A$
Explicit computation of the A_∞-algebra E_θ for KLR algebras when θ is a positive root in type A or of type A2 shows it is torsion-free and intrinsically formal, with a general example of non-formality.