paper

Unbraiding the braided tensor product

arXiv:math/0007174 · doi:10.1063/1.1522818

Abstract

We show that the braided tensor product algebra $A_{1} \otimes A_{2}$ of two module algebras $A_{1}, A_{2}$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_{1}$ with a subalgebra of $A_{1} \otimes A_{2}$ isomorphic to $A_{2}$ , provided there exists a realization of $H$ within $A_{1}$ . In other words, under this assumption we construct a transformation of generators which `decouples' $A_{1}, A_{2}$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.

LaTex file, 29 pages