The note highlights how minimal A-infinity-algebras and obstruction theory classify derived endomorphism algebras of cluster tilting objects.
The Derived Auslander--Iyama Corresponence, a recent result of the authors, provides a classification up to quasi-isomorphism of the derived endomorphism algebras of basic dZ-cluster tilting objects in Hom-finite algebraic triangulated categories in terms of a small amount of algebraic data. In this note we highlight the role of minimal A_∞-algebra structures in the proof of this result, as well as the crucial role of the enhanced A_∞-obstruction theory developed by the second-named author.
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Jasso et al. (2025) studied this question.
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