Self-injective algebras under derived equivalences

TL;DR

This paper demonstrates that properties like weak symmetry and self-injectivity are preserved under derived equivalences in finite-dimensional algebras, and explores the conjugacy of Nakayama permutations in self-injective Artin algebras.

Contribution

It provides an elementary proof that weak symmetry and self-injectivity are invariant under derived equivalences and discusses the conjugacy of Nakayama permutations.

Findings

Weak symmetry and self-injectivity are preserved under derived equivalences.

Nakayama permutations of derived equivalent self-injective Artin algebras are conjugate.

Elementary approach to invariance of algebra properties under derived equivalences.

Abstract

The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an arbitrary field are preserved under derived equivalences.