Minimal ${A}_{\infty}$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917185238073344 |
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| author | Jasso, Gustavo Muro, Fernando |
| author_facet | Jasso, Gustavo Muro, Fernando |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimal ${A}_{\infty}$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects Jasso, Gustavo Muro, Fernando Representation Theory Primary: 18G80. Secondary: 18N40 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. |
| title | Minimal ${A}_{\infty}$-algebras of endomorphisms: The case of $d\mathbb{Z}$-cluster tilting objects |
| topic | Representation Theory Primary: 18G80. Secondary: 18N40 |
| url | https://arxiv.org/abs/2508.18852 |