Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebras

2013/04/18 by Aaron Chan, Chan, Aaron · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1304.5223

openalex publication_date 2013/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The classification of τ-tilting modules over Nakayama algebras
• ν-stable τ-tilting modules
• τ-tilting theory

Cited by

• Efficiency of mutation reduction for Brauer trees
• Two-term tilting complexes over Brauer tree algebras

Related

• An explicit construction of simple-minded systems over self-injective Nakayama algebras
• Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras
• Singularity categories of some 2-CY-tilted algebras
• Singularity Categories of Higher Nakayama Algebras
• The classification of τ-tilting modules over Nakayama algebras