The almost split triangles for perfect complexes over gentle algebras

Abstract

Throughout the paper k denotes a fixed field. All vector spaces and linear maps are k -vector spaces and k -linear maps, respectively. By Z , N , and N + , we denote the sets of integers, nonnegative integers, and positive integers, respectively. For i , j ∈ Z , [ i , j ] : = { l ∈ Z ∣ i ≤ l ≤ j } (in particular, [ i , j ] = ∅ if i > j ).