On the decoupling of the homogeneous and inhomogeneous parts in inhomogeneous quantum groups
نویسندگان
چکیده
منابع مشابه
On the Decoupling of the Homogeneous and Inhomogeneous Parts in Inhomogeneous Quantum Groups
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 Euc...
متن کاملOn the Decoupling of the Homogenous and Inhomogeneous Parts in Inhomogeneous Quantum Groups
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 Euc...
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We briefly report on our result that, if there exists a realization of a Hopf algebra H in a H-module algebra A, then their cross-product is equal to the product of A itself with a subalgebra isomorphic to H and commuting with A. We illustrate its application to the Euclidean quantum groups in N ≥ 3 dimensions.
متن کاملOn the Inhomogeneous Quantum Groups
Using the multi-parametric deformation of the algebra of functions on GL(n + 1) and the universal enveloping algebra U (igl(n+ 1)), we construct the multi-parametric quantum groups IGLq(n) and Uq (igl(n)). The quantization of inhomogeneous groups is not well stablished. These non-semisimple groups are important, both from a purely mathematical point of view , and also because one of the most im...
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It is well known [1, 2] that the Lorentz part of any quantum (or Poisson) Poincaré group is triangular. This is in fact a general feature, which excludes the standard q-deformation from the context of inhomogeneous quantum groups [3]. In order to make the standard q-deformation compatible with inhomogeneous groups one has to consider some generalization of the notion of quantum (Poisson) group,...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2002
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/35/3/312