On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups

Abstract

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$. This result applies in particular to the algebra underlying inhomogeneous quantum groups like the Euclidean ones, which are obtained as cross-products of the quantum Euclidean spaces $R_q^N$ with the quantum groups of rotation $U_{q}so(N)$ of $R_q^N$, for which it has no classical analog.

Latex file, 27 pages. Final version to appear in J. Phys. A

References in corpus (4)

• Field Theory on the q-deformed Fuzzy Sphere I
• Geometrical Tools for Quantum Euclidean Spaces
• Unbraiding the braided tensor product
• Structure of the Three-dimensional Quantum Euclidean Space

Cited by in corpus (7)

• On Iterated Twisted Tensor Products of Algebras
• Unbraiding the braided tensor product
• Representations of cross product algebras of Podles quantum spheres
• Operator representations of cross product algebras of Podles' quantum spheres
• Equivariant Morita equivalences between Podles' spheres
• More examples of invariance under twisting
• Hilbert space representations of cross product algebras II