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Lie Groups Quantum Mathematics Seminar

 Constructing vertex algebras with nonsemisimple category of representations

Simon Lentner, University of Hamburg

Location:  Hill 705
Date & time: Friday, 12 October 2018 at 12:00PM - 1:00PM

  • Abstract :  A long-term goal is to construct vertex algebras, where the category of representations is a finite non-semisimple (modular) tensor category. The main example for such tensor categories on the algebra side are the representations of small quantum groups. In this case, there exists a conjectural construction for a corresponding vertex algebra, as kernel of certain screening operators acting on a lattice vertex algebra (free-field realization). We review some problems and results in this line of researach, in particular the general appearance of quantum group and Nichols algebras in the space of intertwining operators.