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SUMMARY:Frucht theorem for finite quantum groups - Mateusz  Wasilewski (Po
 lish Academy of Sciences)
DTSTART:20241205T100000Z
DTEND:20241205T104000Z
UID:TALK218638@talks.cam.ac.uk
DESCRIPTION:I will report on an on-going project with Michael Brannan\, Da
 niel Gromada\, Junichiro Matsuda\, and Adam Skalski.\n&nbsp\;\nA classical
  result of Frucht says that every finite group can be realized as an autom
 orphism group of a finite graph. Due to Banica and McCarthy\, the followin
 g analogue does not hold: not every finite quantum group is a quantum auto
 morphism group of a finite graph\, e.g. the dual of the permutation group 
 on three generators. Nevertheless we obtained a version of Frucht's theore
 m utilizing quantum graphs: every finite quantum group is a quantum automo
 rphism group of a finite quantum graph. Moreover\, the argument is more ef
 ficient than the original one in the case of classical groups. For a given
  finite quantum group we also tackled the following question: when can we 
 find a quantum Cayley graph\, whose quantum automorphism group is the orig
 inal finite quantum group. I will offer some answers\, mostly for duals of
  classical groups.\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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