Universal localisations and tilting modules for finite dimensional algebras

• Frederik Marks ^[1]
  1. [1] University of Stuttgart

     University of Stuttgart

     Stadtkreis Stuttgart, Alemania

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 7 (July 2015), 2015, págs. 3053-3088
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.10.003
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• Resumen

  • We study universal localisations, in the sense of Cohn and Schofield, for finite dimensional algebras and classify them by certain subcategories of our initial module category. A complete classification is presented in the hereditary case as well as for Nakayama algebras and local algebras. Furthermore, for hereditary algebras, we establish a correspondence between finite dimensional universal localisations and finitely generated support tilting modules. In the Nakayama case, we get a similar result using τ-tilting modules, which were recently introduced by Adachi, Iyama and Reiten.