Singularity categories of derived categories of hereditary algebras are derived categories

2017/02/15 by Yuta Kimura, Kimura, Yuta
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1702.04550

openalex publication_date 2017/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for the path algebra A of an acyclic quiver, the singularity category of the derived category D^{\rm b}(mod A) is triangle equivalent to the derived category of the functor category of \underlinemod A, that is, D_{\rm sg}(D^{\rm b}(mod A))≃ D^{\rm b}(mod(\underlinemod A)). This extends a result of Iyama-Oppermann for the path algebra A of a Dynkin quiver. An important step is to establish a functor category analog of Happel's triangle equivalence for repetitive algebras.

Citations

• Tilting and cluster tilting for preprojective algebras and Coxeter groups
• Singularity categories of representations of algebras over local rings

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