Quasicrossed product on G-graded quasialgebras

TL;DR

This paper introduces the concept of quasicrossed products in G-graded quasialgebras, explores their equivalence with quasicrossed systems, and studies simple structures using graded-bimodules, with a focus on deformed group algebras.

Contribution

It defines quasicrossed products in quasialgebras and establishes their relation to quasicrossed systems, advancing the understanding of graded quasialgebra structures.

Findings

Established the equivalence between quasicrossed products and quasicrossed systems.

Developed the notion of graded-bimodules for analyzing simple quasicrossed products.

Highlighted the role of deformed group algebras in the context of quasialgebras.

Abstract

The notion of quasicrossed product is introduced in the setting of G-graded quasialgebras, i.e., algebras endowed with a grading by a group G, satisfying a "quasiassociative" law. The equivalence between quasicrossed products and quasicrossed systems is explored. It is presented the notion of graded-bimodules in order to study simple quasicrossed products. Deformed group algebras are stressed in particular.