Let A be a finite-dimensional algebra over an algebraically closed field. We study sections in
the Auslander–Reiten quiver of the categories of complexes of fixed size and in the …

By the knitting technique introduced to build the Auslander-Reiten quiver of the category of
complexes of fixed size, it is possible to obtain the Auslander-Reiten triangles in the …

Let A be an additive k-category and C≡ m (A) be the category of m-periodic complexes. For
any integer m> 1, we study conditions under which the compression functor F m: C b (A)→ …

Let Λ be an artin algebra of finite global dimension. We study when the composition of three
irreducible morphisms between indecomposable complexes in K b (proj Λ) is a non-zero …

We study which irreducible morphisms in the category of complexes of fixed size C n (proj A)
with n≥ 2 and A an artin algebra, are irreducible in C [0, n](proj A) or either in C n+ 1 (proj …

Acyclic quantum cluster algebras via Hall algebras of morphisms | Mathematische Zeitschrift
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We investigate the structure of certain almost split sequences in $\mathcal {P}(\Lambda) $,
ie, the category of morphisms between projective modules over an Artin algebra $\Lambda …

For any positive integer n, let A n be a linearly oriented quiver of type A with n vertices. It is
well-known that the quotient of an exact category by projective-injectives is an …

We prove that if the strong global dimension η of an algebra A is finite, then C η+ 1 (proj A) is
of finite type if and only if for each n≥ 2, C n (proj A) is of finite type. Moreover, we also prove …

We consider Λ Λ an artin algebra and n ≥ 2 n≥ 2. We study how to compute the left and
right degrees of irreducible morphisms between complexes in a generalized standard …