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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quantum $n$-space as a quotient of classical $n$-space


Authors: K. R. Goodearl and E. S. Letzter
Journal: Trans. Amer. Math. Soc. 352 (2000), 5855-5876
MSC (2000): Primary 16D60, 16P40, 16S36, 16W35; Secondary 20G42, 81R50
Published electronically: August 8, 2000
MathSciNet review: 1781280
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Abstract: The prime and primitive spectra of $\mathcal{O}_{\mathbf q}(k^{n})$, the multiparameter quantized coordinate ring of affine $n$-space over an algebraically closed field $k$, are shown to be topological quotients of the corresponding classical spectra, $\operatorname{spec} \mathcal{O}(k^{n})$ and $\max \mathcal{O}(k^{n})\approx k^{n}$, provided the multiplicative group generated by the entries of $\mathbf{q}$ avoids $-1$.


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Additional Information

K. R. Goodearl
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: goodearl@math.ucsb.edu

E. S. Letzter
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Address at time of publication: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
Email: letzter@math.tamu.edu, letzter@math.temple.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02639-8
PII: S 0002-9947(00)02639-8
Received by editor(s): April 22, 1999
Published electronically: August 8, 2000
Additional Notes: The research of the first author was partially supported by NSF grant DMS-9622876, and the research of the second author was partially supported by NSF grant DMS-9623579.
Article copyright: © Copyright 2000 American Mathematical Society