Silting reduction and Calabi--Yau reduction of triangulated categories

By Osamu Iyama, Dong Ping Yang. 2014

116 citations recorded by the source corpus.

It is shown that the silting reduction $\ct/\thick\cp$ of a triangulated category $\ct$ with respect to a presilting subcategory $\cp$ can be realized as a certain subfactor category of $\ct$, and that there is a one-to-one correspondence between the set of (pre)silting subcategories of $\ct$ containing $\cp$ and the set of (pre)silting subcategories of $\ct/\thick\cp$. This is analogous to a result for Calabi-Yau reduction. This result is applied to show that Amiot-Guo-Keller's construction of $d$-Calabi-Yau triangulated categories with $d$-cluster-tilting objects takes silting reduction to Calabi-Yau reduction.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/526484b202f0e9178bf9d7e300231505379f3868

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

  1. Thomas Brustle
  2. Dong Yang
  3. Sotaro Asai
  4. Alexander Garver
  5. Thomas McConville

In Geometry and Topology

  1. Thomas Brustle
  2. Dong Yang
  3. Sotaro Asai
  4. Alexander Garver
  5. Thomas McConville

In Statistical and Nonlinear Physics

  1. Thomas Brustle
  2. Dong Yang

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