(G, φ)-crossed product on (G, φ)-quasiassociative algebras

Abstract

The notions of (G, φ)-crossed product and quasicrossed system are introduced in the setting of (G, φ)-quasiassociative algebras, i.e., algebras endowed with a grading by a group G, satisfying a “quasiassociative” law. It is presented two equivalence relations, one for quasicrossed systems and another for (G, φ)-crossed products. Also the notion of graded-bimodule in order to study simple (G, φ)-crossed products is studied.