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SUMMARY:Anna Pachol (University of South-Eastern Norway)
DTSTART:20230726T160000Z
DTEND:20230726T170000Z
DTSTAMP:20260423T040008Z
UID:TQFT/92
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TQFT/92/">Qu
 antum groups in the digital setting</a>\nby Anna Pachol (University of Sou
 th-Eastern Norway) as part of Topological Quantum Field Theory Club (IST\,
  Lisbon)\n\n\nAbstract\nThe main idea behind noncommutative geometry is to
  “algebralize” geometric notions and then generalize them to noncommut
 ative algebras. This way noncommutative geometry offers a generalised noti
 on of the geometry. Quantum groups or Hopf algebras play the role of ‘gr
 oup objects’ in noncommutative geometry and they provide an approach to 
 the development of the theory much as Lie groups do in differential geomet
 ry.\n\nI will give an introduction to the topic and briefly mention result
 s on classification of all bialgebras and Hopf algebras of dimension ≤ 4
  over the field $F_2 = \\{0\, 1\\}$. These results can be summarized as a 
 quiver\, where the vertices are the inequivalent algebras and there is an 
 arrow for each inequivalent bialgebra or Hopf algebra built from the algeb
 ra at the source of the arrow and the dual of the algebra at the target of
  the arrow. There are 314 distinct bialgebras and\, among them\, 25 Hopf a
 lgebras\, with at most one of these from one vertex to another. We found a
  unique smallest noncommutative and noncocommutative quantum group\, which
  is moreover self-dual and resembles a digital version of $U_q(\\mathfrak{
 sl}_2)$.\n
LOCATION:https://researchseminars.org/talk/TQFT/92/
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