Rigidity of tilting complexes and derived equivalence for self-injective algebras

TL;DR

This paper proves that the class of self-injective finite-dimensional algebras over an algebraically closed field remains invariant under derived equivalence, using the concept of rigidity of tilting complexes.

Contribution

It introduces a proof leveraging tilting complex rigidity to establish the invariance of self-injective algebras under derived equivalence.

Findings

Self-injective algebras are closed under derived equivalence

Rigidity of tilting complexes is key to the proof

Provides a new perspective on derived invariance

Abstract

We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.