turkmath.org

In a ring where the multiplicative structure is complicated, it is possible to consider an embedding into another ring where the prior complications do not appear. The latter is named "Ghost Ring". In this talk we will present two ghost rings for the bifree double Burnside ring from a paper by Robert Boltje and Susanne Danz in which this concept is used to prove semisimplicity for the bifree double Burnside ring. We will also give a ghost ring for the bifree monomial double Burnside ring. Our motive is to prove semisimplicity for the bifree p-permutation category, to which a surjection from the bifree monomial Burnside category exists.