Tilting Modules Arising from Two-Term Tilting Complexes

Abstract

We show that every two-term tilting complex over an Artin algebra has a tilting module over a certain factor algebra as a homology group. Also, we determine the endomorphism algebra of such a homology group, which is given as a certain factor algebra of the endomorphism algebra of the two-term tilting complex. Thus, every derived equivalence between Artin algebras given by a two-term tilting complex induces a derived equivalence between the corresponding factor algebras.

Key Words:

• Tilting complex
• Tilting module
• Torsion theory

2010 Mathematics Subject Classification:

• Primary 16G30, 18E30
• Secondary 18E40

Notes

Communicated by J. L. Gomez Pardo.