An inductive method to lift stable equivalences of Morita type to derived equival

摘要: Given a stable equivalence of Morita type F between two algebras A and B, we show that F lifts to a derived equivalence provided that certain restricted stable equivalence of Morita type F' between eAe and fBf lifts to a derived equivalence, where e and f are certain idempotents. As a consequence, all stable equivalences of Morita type between Frobenius-finite algebras(including all algebras of finite representation type, Auslander algebra, cluster-tilted algebra, etc.) lift to derived equivalences. This also gives us an inductive method to lift stable equivalences of Morita type to derived equivaelnces.