A Ringel duality formula inspired by Knörrer equivalences for 2d cyclic quotient singularities

26 January 2017
Martin Kalck

We construct triangle equivalences between singularity categories of
two-dimensional cyclic quotient singularities and singularity categories of
a new class of finite dimensional local algebras, which we call Knörrer
invariant algebras. In the hypersurface case, we recover a special case of Knörrer’s equivalence for (stable) categories of matrix factorisations.
We’ll then explain how this led us to study Ringel duality for
certain (ultra strongly) quasi-hereditary algebras.
This is based on joint work with Joe Karmazyn.

  • Representation Theory Seminar