Derived recollements and generalised AR formulas

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Abstract

The Defect Recollement, Restriction Recollement, Auslander–Gruson–Jensen Recollement, and others, are shown to be instances of a general construction using zeroth derived functors and methods from stable module theory. The right derived functors Wk:=Rk(_) are computed and it is shown that the functor W2:=R2(_) is right exact and restricts to a duality W of the defect zero functors. The duality W satisfies two identities which we call the Generalised Auslander–Reiten formulas. We show that W induces the generalised Auslander–Bridger transpose and show that the Generalised Auslander–Reiten formulas reduce to the well-known Auslander–Reiten formulas.

Bibliographical metadata

Original languageEnglish
JournalJournal of Pure and Applied Algebra
Early online date3 May 2018
DOIs
Publication statusPublished - 2018