JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (4): 67-71.doi: 10.6040/j.issn.1671-9352.0.2018.158

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Complements of partial silting objects in triangulated categories

LIU Hong-jin1,2, LIU Li-min1   

  1. 1. School of Mathematics and Information Engineering, Longyan University, Longyan 364012, Fujian, China;
    2. College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, Fujian, China
  • Published:2019-04-08

Abstract: The existence of the complements of the presilting object P in a Krull-Schmidt triangulated category with a silting object T is investigated. It is shown that if all the indecomposable direct summands of P are generalized two-term related to T, then there exist complements of P. Consequently, P is partial silting. As an application, the presilting complexes over algebras which are derived equivalent to hereditary algebras are partial silting complexes.

Key words: silting objects, presilting objects, complements

CLC Number: 

  • O154.1
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