On Iterated Almost ν-Stable Derived Equivalences

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.

Key Words:

• Derived equivalence
• Stable equivalence of Morita type
• Tilting complex

2010 Mathematics Subject Classification:

• 18E30
• 16G10
• 18G20
• 16D90

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.