Stable categories and reconstruction (Q514206)

The paper aims at a Morita theory for stable equivalence between self-injective algebras \(A\) and \(B\). Suppose that the images of the simple \(B\)-modules under a stable equivalence are given as objects in the stable category over \(A\). It is proved that the associated graded algebra of \(B\) can be reconstructed. A similar question is addressed for the bounded derived category over \(A\), elaborating on previous work by the first author on symmetric algebras [J. Algebra 257, No. 2, 460--481 (2002; Zbl 1033.20005)].