A bicovariant differential algebra of a quantum group |
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| Affiliation: | 1. Department of Physics, Chalmers University of Technology, Gothenburg SE-41296, Sweden;2. Department of Industrial and Materials Science, Chalmers University of Technology, Gothenburg SE-41296, Sweden;3. China Academy of Engineering Physics, Institute of Nuclear Physics and Chemistry, Mianyang 621999, People’s Republic of China;4. Rutherford Appleton Laboratory, ISIS Facility, Didcot OX11 0QX, UK;5. University of Malta, Msida, MSD 2080, Malta;6. Nelson Mandela University, University Way, Summerstrand, Port Elizabeth 6019, South Africa;1. IMSIA, ENSTA Paris-CNRS-EDF-CEA, Institut Polytechnique de Paris, 828 Boulevard des Maréchaux, Palaiseau Cedex 91762, France;2. Laboratoire d’Acoustique de l’Université du Mans, UMR CNRS 6613, Avenue Olivier Messiaen, Le Mans, Cedex 09 72085, France |
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| Abstract: | A bicovariant differential algebra of four basic objects (coordinate functions, differential 1-forms, Lie derivatives and inner derivations) within a differential calculus on a quantum group is shown to be produced by a direct application of the cross-product construction to the Woronowicz differential complex, whose Hopf algebra properties account for the bicovariance of the algebra. A correspondence with classical differential calculus, including Cartan identity, and some other useful relations are considered. An explicit construction of a bicovariant differential algebra on GLq(N) is given and its (co)module properties are discussed. |
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