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SUMMARY:Edmund Heng (IHES)
DTSTART:20250305T100000Z
DTEND:20250305T110000Z
DTSTAMP:20260423T035638Z
UID:EQuAL/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EQuAL/37/">1
 -step beyond semisimple algebras: fusion quivers</a>\nby Edmund Heng (IHES
 ) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nThe 
 study of module categories over fusion categories have focussed mostly on 
 the semisimple ones. In this talk I will introduce the notion of fusion qu
 ivers and their representations\, the categories of which form hereditary 
 (global projective dimension 1) abelian module categories over fusion cate
 gories. This naive “one-step” generalisation from semisimple module ca
 tegories uncovers a wealth of interesting new connections to Coxeter theor
 y. In particular\, I will present a classification result in the spirit of
  Gabriel: the finite-representation-type fusion quivers are classified by 
 the Coxeter—Dynkin diagrams\; the latter includes the (crystallographic)
  Dynkin diagram from Lie algebras ABCDEFG and\, perhaps surprisingly\, als
 o the non-crystallographic diagrams H and I\, which all together classify 
 the finite Coxeter groups. This is based on joint work with Ben Elias.\n
LOCATION:https://researchseminars.org/talk/EQuAL/37/
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