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

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

2001-01-26

arxiv.org/abs/math/0101218v2

Mathematics

Quantum Algebra

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

Scientific paper

10.1088/0305-4470/35/3/312

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 $U_qso(N)$ of $R_q^N$, for which it has no classical analog.

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