Almost \cal D-split sequences and derived equivalences

2008/10/27 by Wei Hu, Hu, Wei, Changchang Xi +1
Mathematics · Physics and Astronomy · #16G70 #18E30 (Primary) 16G10 #18G20 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:16G10 #msc:16G70 #msc:18E30 #msc:18G20

paper · pdf · doi:10.48550/arxiv.0810.4757

arxiv created 2008/10/27 · openalex publication_date 2008/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce almost \cal D-split sequences and establish an elementary but somewhat surprising connection between derived equivalences and Auslander-Reiten sequences via BB-tilting modules. In particular, we obtain derived equivalences from Auslander-Reiten sequences (or n-almost split sequences), and Auslander-Reiten triangles.

Related

• Determination of some almost split sequences in morphism categories
• The Auslander-Reiten theory of the morphism category of projective modules
• Almost split sequences and approximations
• Cotorsion pairs associated with Auslander categories
• Auslander-Reiten theory via Nakayama duality in abelian categories