The Auslander-Reiten formula for complexes of modules

2004/12/04 by Henning Krause, Krause, Henning, Jue Le +1
Mathematics · #16G70 #18E30 #18G10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16G70 #msc:18E30 #msc:18G10

paper · pdf · doi:10.48550/arxiv.math/0412085

published in arXiv (Cornell University) (Cornell University) · 14 pages

openalex publication_date 2004/12/04 · arxiv created 2004/12/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

An Auslander-Reiten formula for complexes of modules is presented. This formula contains as a special case the classical Auslander Reiten formula. The Auslander-Reiten translate of a complex is described explicitly, and various applications are discussed.

Citations

• Representation Theory of Artin Algebras
• Deriving DG categories

Related

• The Auslander Bound for Complexes
• The Auslander bijections: How morphisms are determined by modules
• On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras
• Derived Recollements and Generalised AR Formulas
• Algebraic Modules and the Auslander--Reiten Quiver