The classification of τ-tilting modules over Nakayama algebras

2013/09/09 by Takahide Adachi, Adachi, Takahide · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1309.2216

openalex publication_date 2013/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study tau-tilting modules over Nakayama algebras. We establish bijections between tau-tilting modules, triangulations of a polygon with a puncture and certain integer sequences. Moreover, we give an algorithm to construct the Hasse quiver of support tau-tilting modules by using Rejection Lemma of Drozd-Kirichenko.

Citations

• τ-rigid modules for algebras with radical square zero

Cited by

• A class of Nakayama algebras with a braid group action on τ-exceptional sequences
• ν-stable τ-tilting modules
• Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebras

Related

• Tau-tilting modules over trivial extenstions
• Taking tilting modules from the poset of support tilting modules
• Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras
• A note on the Hasse quiver of τ-tilting modules
• ν-stable τ-tilting modules