Abstract
In this article, by characterizing iterated almost ν-stable derived equivalences, we give several sufficient conditions for a derived equivalence between general finite-dimensional algebras to induce a stable equivalence of Morita type. In particular, we prove the following: Let A and B be two finite-dimensional algebras over a field. Suppose that there is a derived equivalence between A and B induced by a tilting complex T
• over A. If each indecomposable projective A-module P without the property “ is projective for all i ≥ 0” occurs only in the 0-degree term T
0 of T
• with multiplicity 1, then A and B are stably equivalent of Morita type.
ACKNOWLEDGMENT
This work is partially supported by China Postdoctoral Science Foundation (No. 20080440003) and SRFDP (No. 20100003120004). The author also thanks the Alexander von Humboldt Foundation for support.
Notes
Communicated by Q. Wu.