Silting reduction and Calabi--Yau reduction of triangulated categories

2014/08/12 by Osamu Iyama, Dong Yang, Iyama, Osamu +1 · 6 citations
Mathematics · #13F60 #16E35 #16G99 #18E30 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:13F60 #msc:16E35 #msc:16G99 #msc:18E30

paper · pdf · doi:10.48550/arxiv.1408.2678

Section 5.5 in v4 removed: the formula (5.5.1) was a misunderstanding of the cited result in [KR1]. To appear in TAMS

arxiv created 2018/04/29 · arxiv updated 2018/05/01

Abstract

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.

Cited by

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• Proper modules over Ginzburg dg algebras and compact Fukaya categories of plumbings
• Classification of silted algebras for two quivers of Dynkin type \mathbbA_n
• Equivariant recollements and singular equivalences

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