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arXiv · 2505.16560

On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras

Nao Mochizuki·Marvin Plogmann
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Abstract

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.

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BibTeXRIS

Nao Mochizuki, Marvin Plogmann. 2025-05-22. On the Auslander--Reiten Theory for Extended Hearts of Proper Connective DG Algebras. https://arxiv.org/abs/2505.16560

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