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

Previous Articles     Next Articles

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

PDF (PC)

598

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
[1] HAPPEL D, RINGEL C M. Tilted algebras[J]. Trans Amer Math Soc, 1982, 274(2):339-443.
[2] KELLER B, VOSSIECK D. Aisles in derived categories[J]. Bull Soc Math Belg: Ser A, 1988, 40(2):239-253.
[3] AIHARA T, IYAMA O. Silting mutation in triangulated categories[J]. J Lond Math Soc, 2012, 85(3):633-668.
[4] AIHARA T, IYAMA O, REITEN I. τ-tilting theory[J]. Compos Math, 2014, 150(3):415-452.
[5] IYAMA O, JORGENSEN P, YANG D. Intermediate co-t-structures, two-term silting objects, τ-tilting modules, and torsion classes[J]. Algebra Number Theory, 2014, 8(10):2413-2431.
[6] AIHARA T, MIZUNO Y. Classifying tilting complexes over preprojective algebras of Dynkin type[J]. Algebra Number Theory, 2017, 11(6):1287-1315.
[7] BONGARTZ K. Tilted algebras[M] // Proc ICRA Ⅲ(Puebla, 1980), Lecture Notes in Math, vol. 903. New York: Springer, 1981: 26-38.
[8] LI Shen, ZHANG Shunhua. Some applications of τ-tilting theory[J/OL].[2015-12-11]. arXiv: 1512.03613v1. https://arxiv.org/pdf/1512.03613.pdf.
[9] AIHARA T. Tilting-connected symmetric algebras[J]. Algebra Representation Theory, 2013, 16(3):873-894.
[10] BUAN A B. Subcategories of the derived category and cotilting complexes[J]. Colloq Math, 2001, 88(1):1-11.
[11] RICKARD J. Morita theory for derived categories[J]. J Lond Math Soc, 1989, 39(2):436-456.
[12] HAPPEL D. Triangulated categories in the representation theory of finite-dimensional algebras[M] // London Mathematical Society Lecture Note Series, 119. Cambridge: Cambridge University Press, 1988.
[1] LEI Xue-ping. Almost complete C-tilting modules [J]. J4, 2011, 46(2): 101-104.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LIU Fang-yuan, MENG Xian-jia, TANG Zhan-yong, FANG Ding-yi, GONG Xiao-qing. Android application protection based on smali code obfuscation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 44 -50 .
[2] LIAO Xiang-wen, ZHANG Ling-ying, WEI Jing-jing, GUI Lin, CHENG Xue-qi, CHEN Guo-long. User influence analysis of social media with temporal characteristics[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(3): 1 -12 .
[3] GU Shen-ming, LU Jin-lu, WU Wei-zhi, ZHUANG Yu-bin. Local optimal granularity selections in generalized multi-scale decision systems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 1 -8 .
[4] YE Xiao-ming, CHEN Xing-shu, YANG Li, WANG Wen-xian, ZHU Yi, SHAO Guo-lin, LIANG Gang. Anomaly detection model of host group based on graph-evolution events[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(9): 1 -11 .
[5] Zhao-xia WU,Jia-qi WANG. Wireless single spectrum secure auction algorithm[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 51 -55 .
[6] WAN Peng-fei, GAO Xing-bao. Novel artificial bee colony algorithm based on objective space decomposition for solving multi-objective optimization problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(11): 56 -66 .
[7] CAO Wei-dong, DAI Tao, YU Jin-biao, WANG Xiao-hong, SHI An-feng. Improvement on the solution of pressure equation based on alternating direction in chemical flooding model[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 88 -94 .
[8] LI Jin-hai, WU Wei-zhi. Granular computing approach for formal concept analysis and its research outlooks[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 1 -12 .
[9] SUN Jian-dong, GU Xiu-sen, LI Yan, XU Wei-ran. Chinese entity relation extraction algorithms based on COAE2016 datasets[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 7 -12 .
[10] SHAO Yong. Semilattice-ordered completely regular periodic semigroups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 1 -5 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd