Abstract
The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other (η) expressing the quantum groups as “deformation” of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the η-deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.
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Dedicated to Asim Barut with all our friendship.
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Flato, M., Lu, ZC. & Sternheimer, D. From where do quantum groups come?. Found Phys 23, 587–598 (1993). https://doi.org/10.1007/BF01883767
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DOI: https://doi.org/10.1007/BF01883767