Decoupling of Tensor factors in Cross Product and Braided Tensor Product Algebras

We briefly review and illustrate our procedure to ‘decouple’ by transformation of generators: either a Hopf algebra $H$ from a $H$-module algebra $A_1$ in their cross-product $A_1>◃H$; or two (or more) $H$-module algebras $A_1,A_2$. These transformations are based on the existence of an algebra map $A_1>◃H\to A_1$.