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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Relative cluster categories and Higgs categories w
ith infinite-dimensional morphism spaces. - Yilin
Wu (Université Paris 7 - Denis-Diderot\, East Chin
a Normal University)
DTSTART;TZID=Europe/London:20211126T160000
DTEND;TZID=Europe/London:20211126T170000
UID:TALK164911AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/164911
DESCRIPTION:Cluster categories were introduced in 2006 by Buan
-Marsh-Reineke-Reiten-Todorov in order to categori
fy acyclic cluster algebras without coefficients.
Their construction was generalized by Amiot to Jac
obi-finite quiver with potential (2009). Later\, P
lamondon generalized it to arbitrary cluster algeb
ras associated with quivers (2009 and 2011). Clust
er algebras with coefficients are important since
they appear in nature as coordinate algebras of va
rieties like Grassmannians\, double Bruhat cells\,
unipotent cells\,... The work of Geiss-Leclerc-Sc
hrö\;er often yields Frobenius exact categorie
s which allow to categorify such cluster algebras.
In previous work\, we have constructed Higgs cate
gories and relative cluster categories in the Jaco
bi-finite setting (arXiv:2109.03707). Higgs catego
ries generalize the Frobenius categories used by G
eiss-Leclerc-Schrö\;er.\nIn this talk\, we wil
l present the construction of the Higgs category a
nd of the relative cluster category in the Jacobi-
infinite setting. As in the Jacobi-finite case\, t
he Higgs category is no longer exact but still ext
riangulated in the sense of Nakaoka-Palu (2019). W
e will also give the construction of a cluster cha
racter in this setting.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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