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SUMMARY:The Ginzburg embedding of a proper Higgs category [Oberseminar Alg
 ebra und Darstellungstheorie]
DTSTART:20261022T141500Z
DTEND:20261022T151500Z
DTSTAMP:20261101T232400Z
UID:indico-event-1673@math-events.uni-bonn.de
DESCRIPTION:Speakers: Yifei Cheng (Université Paris Cité)\n\nHiggs categ
 ories were defined by Yilin Wu\, who used them to categorify cluster algeb
 ras with coefficients. In his construction\, the Ginzburg morphism plays a
 n important role\, as it carries a left 3-Calabi-Yau structure. Using the 
 restriction functor along this morphism\, we show that each proper Higgs c
 ategory H embeds into the derived category of a derived preprojective alge
 bra A of Dynkin type. More precisely\, the Ginzburg morphism induces a 1-t
 runcated dg equivalence from H onto an extension closed subcategory of the
  perfectly valued derived category of A. As a corollary\, we show that the
  Hom-finite Quillen exact Higgs categories are exactly the subcategories o
 f the module categories over classical preprojective algebras considered b
 y Geiss-Leclerc-Schröer and Buan-Iyama-Reiten-Scott/Smith. Finally\, we c
 alculate the image of the Higgs categories through this embedding functor 
 in certain cases. This leads us to a dg generalization of the classical co
 nstructions of stably 2-Calabi-Yau Frobenius extriangulated categories wit
 h cluster tilting objects. This is a report on my ongoing Ph.D. thesis sup
 ervised by Bin Zhu and Bernhard Keller.\n\nhttps://math-events.uni-bonn.de
 /event/1673/
LOCATION:Endenicher Allee 60/1-008 - Seminarraum (Mathezentrum) (Mathezent
 rum)
URL:https://math-events.uni-bonn.de/event/1673/
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