We investigate the relationship between level of a bounded complex over commutative ring with respect to class Gorenstein projective modules and other invariants or ring, such as dimension, Krull dimension. The results build upon work done by J. D. Christensen [7], H. Altmann et al. [1], Avramov [4] for levels finitely generated modules.

We first introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category. This unifies the notion of an almost split sequence in an abelian category and that of an Auslander-Reiten triangle in a triangulated category. We then define the Auslander-Reiten quiver of a Krull-Schmidt category and describe the shapes of its semi-stable components. The main result generalizes those fo...