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Two-term Tilting Complexes and Simple-minded Systems of Self-injective Nakayama Algebras

Abstract

We study the relation between simple-minded systems and two-term tilting complexes for self-injective Nakayama algebras. More precisely, we show that any simple-minded system of a self-injective Nakayama algebra is the image of the set of simple modules under a stable equivalence, which is given by the restriction of a standard derived equivalence induced by a two-term tilting complex. We achieve this by exploiting and connecting the mutation theories from the combinatorics of Brauer tree, configurations of stable translations quivers of type A, and triangulations of a punctured convex regular polygon.

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Correspondence to Aaron Chan.

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Presented by Claus Michael Ringel

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Chan, A. Two-term Tilting Complexes and Simple-minded Systems of Self-injective Nakayama Algebras. Algebr Represent Theor 18, 183–203 (2015). https://doi.org/10.1007/s10468-014-9487-6

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Keywords

  • Simple-minded system
  • (Two-term) tilting complex
  • Brauer tree
  • Configuration
  • Triangulation
  • Mutation.

Mathematics Subject Classifications (2010)

  • 16G10
  • 18E30