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    Semiclassical limits of quantum affine spaces

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    Genre
    Journal Article
    Date
    2009-06-01
    Author
    Goodearl, KR
    Letzter, ES
    Subject
    quantum affine space
    prime and primitive spectra
    Poisson-prime and Poisson-primitive spectra
    symplectic core
    semiclassical limit
    quantum toric variety
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6072
    
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    DOI
    10.1017/S0013091507000910
    Abstract
    Semiclassical limits of generic multi-parameter quantized coordinate rings A=Oq(kn) of affine spaces are constructed and related to A, for k an algebraically closed field of characteristic zero and q a multiplicatively antisymmetric matrix whose entries generate a torsion-free subgroup of k. A semiclassical limit of A is a Poisson algebra structure on the corresponding classical coordinate ring R=O(kn), and results of Oh, Park, Shin and the authors are used to construct homeomorphisms from the Poisson-prime and Poisson-primitive spectra of R onto the prime and primitive spectra of A. The Poisson-primitive spectrum of R is then identified with the space of symplectic cores in kn in the sense of Brown and Gordon, and an example is presented (over ℂ) for which the Poisson-primitive spectrum of R is not homeomorphic to the space of symplectic leaves in kn. Finally, these results are extended from quantum affine spaces to quantum affine toric varieties. © Edinburgh Mathematical Society 2009.
    Citation to related work
    Cambridge University Press (CUP)
    Has part
    Proceedings of the Edinburgh Mathematical Society
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/6054
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