Simple-minded systems, configurations and mutations for representation-finite self-injective algebras

• Aaron Chan ^[1] ; Steffen Koenig ^[2] ; Yuming Liu ^[3]
  1. [1] University of Aberdeen

     University of Aberdeen

     Reino Unido

     
  2. [2] University of Stuttgart

     University of Stuttgart

     Stadtkreis Stuttgart, Alemania

     
  3. [3] Beijing Normal University

     Beijing Normal University

     China

     

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• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 1940-1961
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.07.018
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• Resumen

  • Simple-minded systems of objects in a stable module category are defined by common properties with the set of simple modules, whose images under stable equivalences do form simple-minded systems. Over a representation-finite self-injective algebra, it is shown that all simple-minded systems are images of simple modules under stable equivalences of Morita type, and that all simple-minded systems can be lifted to Nakayama-stable simple-minded collections in the derived category. In particular, all simple-minded systems can be obtained algorithmically using mutations.