On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916805052727296 |
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| author | Mochizuki, Nao Plogmann, Marvin |
| author_facet | Mochizuki, Nao Plogmann, Marvin |
| contents | We prove that, for a proper connective dg algebra $A$ with cohomology concentrated in degrees between $1-d$ and $0$, the extended heart $\mathcal{D}^{fd}(A)^{(-d,0]}\subseteq \mathcal{D}^{fd}(A)$ is an extriangulated category with almost-split conflations. We also prove a version of the 1st Brauer--Thrall Conjecture in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras Mochizuki, Nao Plogmann, Marvin Representation Theory Primary: 18G80. Secondary: 16E45, 16G70 We prove that, for a proper connective dg algebra $A$ with cohomology concentrated in degrees between $1-d$ and $0$, the extended heart $\mathcal{D}^{fd}(A)^{(-d,0]}\subseteq \mathcal{D}^{fd}(A)$ is an extriangulated category with almost-split conflations. We also prove a version of the 1st Brauer--Thrall Conjecture in this context. |
| title | On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras |
| topic | Representation Theory Primary: 18G80. Secondary: 16E45, 16G70 |
| url | https://arxiv.org/abs/2505.16560 |