… Auslander-Reiten sequences and we show how to compute them in terms of reflection functors.
In … In the latter case, we calculate the coordinates of the Auslander-Reiten translation of a …

… Auslander-Reiten sequences In § 1 we worked out a construction of the Auslander-Reiten
sequence … Reflection-functors. For the sake of completeness we recall the orizinal description …

… functors C’(C), ie, the composite of the reflection functors through an +(-) admissible
sequence of vertices, are equivalent to the Auslander-Reiten translations DT:(T,DA) which play a …

… B of A is such that a functor in mod A restricts to a functor in mod B. Under these circumstances,
… functors vanishing on B. We then have the usual exact sequence of Grothendieck groups …

… is the natural epimorphism, [3 the negative of the inclusion, are AuslanderReiten sequences.
Proof: Induction on length n of P If 1(p) is 2 it is true,that is an Auslander-Reiten sequence. …

… HC are finitely generated modules over the center of R and provides a duality functor D :
mod(R) → mod(Rop). We show that the Serre functor SA induces a Serre functor SC : Proj(HC) …

… The construction of the reflection functors In this paper all rings which are considered are …
artin algebras~ irreducible maps, Auslander-Reiten sequences, transpose and dual transpose …

… a generalisation of the higher reflection functors of Iyama and … exact functor(1.2) G : mod
A ⟶ mod Γ , X ↦ Hom A ( M , X ) . Notably, under the functor G, the almost split exact sequences …

… We call this the reflection of 𝒞. Dually, we define an augmented functor to be an additive
endofunctor S together with a natural transformation S → 1. So the counit of a coreflective full …

… reflection functors to the valued case, including the description of their behavior on simple
representations, as well as some properties of the composition of reflection functors, … reflection …