Graded equivalence theory with applications
Abstract
We develop the foundations for graded equivalence theory and apply them to
investigate properties such as primeness, finite representation type, and vertex
theory of graded rings. The key fact that we prove is that, for any two G-graded
rings R and S such that there is a category equivalence from gr(R) to gr(S) that
commutes with suspensions, then, for any subgroup H of G, the categories
gr(HIG, R) and gr(HIG, S) of modules graded by the G-set of right cosets are
also equivalent.