The Ginzburg embedding of a proper Higgs categoryOberseminar Algebra und Darstellungstheorie

by Yifei Cheng (Université Paris Cité)

Thursday Oct 22, 2026, 4:15 PM → 5:15 PM Europe/Berlin

Endenicher Allee 60/1-008 - Seminarraum (Mathezentrum) (Mathezentrum)

Higgs categories were defined by Yilin Wu, who used them to categorify cluster algebras with coefficients. In his construction, the Ginzburg morphism plays an important role, as it carries a left 3-Calabi-Yau structure. Using the restriction functor along this morphism, we show that each proper Higgs category H embeds into the derived category of a derived preprojective algebra A of Dynkin type. More precisely, the Ginzburg morphism induces a 1-truncated 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 of the module categories over classical preprojective algebras considered by Geiss-Leclerc-Schröer and Buan-Iyama-Reiten-Scott/Smith. Finally, we calculate the image of the Higgs categories through this embedding functor in certain cases. This leads us to a dg generalization of the classical constructions of stably 2-Calabi-Yau Frobenius extriangulated categories with cluster tilting objects. This is a report on my ongoing Ph.D. thesis supervised by Bin Zhu and Bernhard Keller.