2001/01/31 by Gaetano Fiore · 17 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Division algebra #Euclidean geometry #Euclidean group #Geometry #Hopf algebra #Mathematics #Physics #Pure mathematics #Quantum #Quantum group #Quantum mechanics #Realization (probability) #Subalgebra #Tensor algebra #Tensor product #math.GR #math.QA #msc:17B37 #msc:81R50
paper · pdf · doi:10.1088/0305-4470/35/3/312
published in Journal of Physics A Mathematical and General 35(3), 657-678 (Institute of Physics) · Latex file, 27 pages. Final version to appear in J. Phys. A
arxiv created 2001/12/21 · openalex publication_date 2002/01/14 · arxiv updated 2012/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that, if there exists a realization of a Hopf algebra H in a H -module algebra , then one can split their cross-product into the tensor product algebra of itself with a subalgebra isomorphic to H and commuting with . This result applies in particular to the algebra underlying inhomogeneous quantum groups like the Euclidean groups, which are obtained as cross-products of the quantum Euclidean spaces q N with the quantum groups of rotation U q so ( N ) of q N , for which it has no classical analogue.