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

2025/05/22 by Mochizuki, Nao, Plogmann, Marvin · 2 citations
#16G70 #FOS: Mathematics #Primary: 18G80. Secondary: 16E45 #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.16560

Abstract

We prove that, for a proper connective dg algebra A with cohomology concentrated in degrees between 1-d and 0, the extended heart D^fd(A)^(-d,0]⊆ 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.

Cited by

• AIR tilting subcategories of extended hearts
• Semibricks and wide subcategories in extended module categories

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