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Unbraiding the braided tensor product

Gaetano Fiore·Harold Steinacker·Julius Wess
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Abstract

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ 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 $A_1\underline{\otimes}A_2$ 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.

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Gaetano Fiore, Harold Steinacker, Julius Wess. 2000-12-20. Unbraiding the braided tensor product. https://doi.org/10.1063/1.1522818

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