Self-injective algebras under derived equivalences

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.

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 229; no. 1; p. 107795
Main Authors Xi, Changchang, Zhang, Jin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.01.2025
Subjects
Derived equivalence
Grothendieck group
Nakayama permutation
Self-injective algebra
Symmetric algebra
Weakly symmetric algebra
secondary
Grothendieck group
Weakly symmetric algebra
Primary
Derived equivalence
Nakayama permutation
Symmetric algebra
Self-injective algebra
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Summary: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.
ISSN:0022-4049
DOI:10.1016/j.jpaa.2024.107795