Derived equivalences between symmetric special biserial algebras

• Takuma Aihara ^[1]
  1. [1] Bielefeld University

     Bielefeld University

     Kreisfreie Stadt Bielefeld, Alemania

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 5 ( (May 2015)), 2015, págs. 1800-1825
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.07.012
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• Resumen

  • The notion of mutation plays crucial roles in representation theory of algebras. Two kinds of mutation are well-known: tilting/silting mutation and quiver-mutation. In this paper, we focus on tilting mutation for symmetric algebras. Introducing mutation of SB quivers, we explicitly give a combinatorial description of tilting mutation of symmetric special biserial algebras. As an application, we generalize Rickard's star theorem. We also introduce flip of Brauer graphs and apply our results to Brauer graph algebras.