Quantum group (CO)actions onG-spaces and quantum modules |
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Authors: | Andreas Arvanitoyeorgos Demosthenes Ellinas |
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Institution: | (1) The British Council-Greece, 17 Kolonaki Square, GR-102 10 Athens, Greece;(2) University of Essex, England;(3) Department of Mathematics, University of Crete, GR-714 09 Heraklion, Crete, Greece |
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Abstract: | A generalized transformation theory is introduced by using quantum (non-commutative) spaces transformed by quantum Lie groups (Hopf algebras). In our method dual pairs of -quantum groups/algebras (co)act on quantum spaces equipped with the structure of a -comodule algebra. We use the quantized groupSU
q
(2) as a show case, and we determine its action on modules such as theq-oscillator and the quantum sphere. We also apply our method for the quantized Euclidean groupF
q
(E(2)) acting on a quantum homogeneous space. For the sphere case the construction leads to an analytic pseudodifferential vector field realization of the deformed algebra su
q
(2) on the quantum projective plane for north and south pole.Presented by A.A. at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–20 June 1996 and by D.E. at the 4th International Congress of Geometry, Thessaloniki. |
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Keywords: | |
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