We introduce the notion of a strong equivalence between graded algebras and prove that any partially-strongly-graded algebra by a group G is strongly-graded-equivalent to the skew group algebra by a product partial action of G. We show that strongly-graded-equivalence preserves strong gradings and is nicely related to Morita equivalence of product partial actions. Furthermore, we show that strongly-graded-equivalent partially-strongly-graded algebras with orthogonal local units are stably isomorphic as graded algebras.
This is a part of a joint preprint with Fernando Abadie and Ruy Exel.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
