\((G,\phi)\)-crossed product on \((G,\phi)\)-quasiassociative algebras

Abstract

The notions of \((G,\phi)\)-crossed product and quasicrossed system are introduced in the setting of \((G,\phi)\)-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 \((G,\phi)\)-crossed products. Also the notion of graded-bimodule in order to study simple \((G,\phi)\)-crossed products is studied.