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Unbounded ladders induced by Gorenstein algebras

Volume 151 / 2018

Pu Zhang, Yuehui Zhang, Guodong Zhou, Lin Zhu Colloquium Mathematicum 151 (2018), 37-56 MSC: 18E30, 16E35, 18A40, 18A22, 16G10. DOI: 10.4064/cm7089-1-2017 Published online: 23 October 2017

Abstract

We prove that the derived category $D(\mathop {\rm Mod}A)$ of a Gorenstein triangular matrix algebra $A$ admits an unbounded ladder. We observe that a left recollement of triangulated categories with Serre functors always sits in a ladder of period $1$. As an application, the singularity category of $A$ admits a ladder of period $1$.

Authors

  • Pu ZhangSchool of Mathematics
    Shanghai Jiao Tong University
    Shanghai 200240, China
    e-mail
  • Yuehui ZhangSchool of Mathematics
    Shanghai Jiao Tong University
    Shanghai 200240, China
    e-mail
  • Guodong ZhouDepartment of Mathematics
    Shanghai Key Lab. of PMMP
    East China Normal University
    Shanghai 200241, China
    e-mail
  • Lin ZhuSchool of Mathematics
    Shanghai Jiao Tong University
    Shanghai 200240, China
    e-mail

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