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SUMMARY:Ilaria Colazzo (University of Leeds)
DTSTART:20260520T090000Z
DTEND:20260520T100000Z
DTSTAMP:20260530T105731Z
UID:EQuAL/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EQuAL/57/">A
  Hopf Algebra Perspective on Set-Theoretic Pentagon Solutions</a>\nby Ilar
 ia Colazzo (University of Leeds) as part of European Quantum Algebra Lectu
 res (EQuAL)\n\n\nAbstract\nIn this talk I will report on joint work with J
 anssens. We investigate the connection between bijective set-theoretic sol
 utions of the pentagon equation and Hopf algebras. In the finite setting\,
  we show that such solutions correspond to Hopf algebras with the positive
  basis property\, and as a corollary we generalise the Lu–Yan–Zhu clas
 sification to arbitrary characteristic 0 fields. We also address the more 
 general question of when a Hopf algebra admits a basis that yields a set-t
 heoretic solution. If time permits\, we will discuss classification result
 s in the (co)commutative case. I will explain the main ideas of the constr
 uctions and illustrate the results with examples.\n
LOCATION:https://researchseminars.org/talk/EQuAL/57/
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