Invariance under twisting for crossed products

TL;DR

This paper proves an invariance property under twisting for Brzezinski's crossed products, unifying and generalizing previous invariance results for various algebraic constructions.

Contribution

It introduces a broad invariance result for crossed products that encompasses several known cases, including twisted tensor products and quasi-Hopf smash products.

Findings

Unifies invariance properties of different algebraic structures

Generalizes invariance under twisting to a broader class of crossed products

Includes as a special case the equivalence of crossed products by a coalgebra

Abstract

We prove a result of the type ''invariance under twisting'' for Brzezinski's crossed products, as a common generalization of the invariance under twisting for twisted tensor products of algebras and the invariance under twisting for quasi-Hopf smash products. It turns out that this result contains also as a particular case the equivalence of crossed products by a coalgebra (due to Brzezinski).