Unbraiding transformations for braided tensor factors

Two quantum group covariant algebras A1, A2 can be embedded in a larger one through the so-called braided tensor product, whereby they do not commute with each other. We briefly report on our transformations of generators8 which allow to express this braided tensor product algebra as an ordinary tensor product algebra of A1 with a subalgebra isomorphic to A2 and commuting with A1. The construction of the transformations is based on the existence of a realization of H within A1. We apply the results to the braided tensor product algebras of two or more quantum group covariant quantum spaces or deformed Heisenberg algebras.