Suitable Topics for Student Projects:

  • Work out explicitely the Nichols algebras for A4 (rank 1) and then for the rack T (rank 2).
  • Work out and decompose the Deligne-Lusztig characters (both ways) for the groups PSL2(4)=PSL2(5)=A5
  • Determine new liftings for certain Nichols algebras from known diagonal liftings, and hence some new pointed Hopf algebras.
  • (*) Attempt the techniques by Heckenberger/Vendramin to determine (and maybe classify) finite-dimensional Nichols algebra over rank 2 racks  (instead of groups)
  • (*) Work out an example of a logarithmic conformal quantum field theory of rank 2 using screening charges.