Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras

2020/10/14 by Xiaojin Zhang, Zhang, Xiaojin
Mathematics · #16E10 #16G10 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:16E10 #msc:16G10

paper · pdf · doi:10.48550/arxiv.2010.07099

6 pages,to appear in Journal of Algebra and Its Applications

arxiv created 2020/10/14 · openalex publication_date 2020/10/14 · arxiv updated 2020/10/15 · openalex created_date 2020/10/22 · openalex updated_date 2026/07/28

Abstract

Let Λ be a radical square zero Nakayama algebra with n simple modules and let Γ be the Auslander algebra of Λ. Then every indecomposable direct summand of a tilting Γ-module is either simple or projective. Moreover, if Λ is self-injective, then the number of tilting Γ-modules is 2ⁿ; otherwise, the number of tilting Γ-modules is 2^n-1.

Related

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• Dominant dimension and tilting modules
• Tilting modules for the Auslander algebra of K[x]/(xⁿ)
• τ-rigid modules for algebras with radical square zero
• The classification of τ-tilting modules over Nakayama algebras