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

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.

20 pages. Added Harada-Sai Lemma and Brauer-Thrall 1 for extended hearts and changed abstract accordingly