Auslander correspondence for proper connective DG-algebras via extended module categories
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917266088525824 |
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| author | Mochizuki, Nao |
| author_facet | Mochizuki, Nao |
| contents | We establish a $d$-dimensional Auslander correspondence for $d$-truncated proper connective DG-algebras via $d$-extended module categories. A $d$-truncated proper connective DG-algebra $Γ$ is called Auslander if its $d$-extended module category is a $d$-Auslander extriangulated category. Our main theorem gives a one-to-one correspondence: for any $d$-truncated proper connective DG-algebra $Λ$ whose $d$-extended module category has finitely many indecomposable objects, the DG-endomorphism algebra of an additive generator is Auslander, and conversely every Auslander $d$-truncated proper connective DG-algebra arises in this way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01761 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Auslander correspondence for proper connective DG-algebras via extended module categories Mochizuki, Nao Representation Theory Category Theory Primary: 18G80. Secondary: 16E45, 16G70 We establish a $d$-dimensional Auslander correspondence for $d$-truncated proper connective DG-algebras via $d$-extended module categories. A $d$-truncated proper connective DG-algebra $Γ$ is called Auslander if its $d$-extended module category is a $d$-Auslander extriangulated category. Our main theorem gives a one-to-one correspondence: for any $d$-truncated proper connective DG-algebra $Λ$ whose $d$-extended module category has finitely many indecomposable objects, the DG-endomorphism algebra of an additive generator is Auslander, and conversely every Auslander $d$-truncated proper connective DG-algebra arises in this way. |
| title | Auslander correspondence for proper connective DG-algebras via extended module categories |
| topic | Representation Theory Category Theory Primary: 18G80. Secondary: 16E45, 16G70 |
| url | https://arxiv.org/abs/2602.01761 |