2007/08/08 by K. R. Goodearl, Goodearl, K. R., Edward S. Letzter +2
Mathematics · #16D60 #16W35 #17B63 #20G42 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16D60 #msc:16W35 #msc:17B63 #msc:20G42
paper · pdf · doi:10.48550/arxiv.0708.1091
20 pages; LaTeX; Xy-pic; 4 diagrams; to appear in Proc. Edinburgh Math. Soc
openalex publication_date 2007/08/08 · arxiv created 2008/02/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Semiclassical limits of generic multiparameter 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 torsionfree 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 the complex numbers) 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.