The diagram for endomorphism algebras of two-term tilting complexes over self-injective algebras

ABSTRACT

We construct a diagram between the endomorphism algebra of a two-term projective module complex over a self-injective algebra and the endomorphism algebras of its homology groups and apply the diagram to the tilting theory of self-injective algebras. We give an example of recovering the endomorphism algebra of a two-term tilting complex over a self-injective algebra from the endomorphism algebras of its homology groups with some additional structures which appear in the diagram.

KEYWORDS:

• Derived category
• tilting complex
• tilting module

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16G30, 18E30
• Secondary 18E40