Minimal ${A}_{\infty}$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects

Gustavo Jasso; Fernando Muro

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arXiv · 2508.18852

Minimal ${A}_{\infty}$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects

Gustavo Jasso·Fernando Muro

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Abstract

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 $d\mathbb{Z}$-cluster tilting objects in $\operatorname{Hom}$-finite algebraic triangulated categories in terms of a small amount of algebraic data. In this note we highlight the role of minimal $A_\infty$-algebra structures in the proof of this result, as well as the crucial role of the enhanced $A_\infty$-obstruction theory developed by the second-named author.

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BibTeX RIS

Gustavo Jasso, Fernando Muro. 2025-08-26. Minimal ${A}_{\infty}$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects. https://arxiv.org/abs/2508.18852

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