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ISSN 1088-6850(e) ISSN 0002-9947(p)

Quantum -space as a quotient of classical -space

Author(s): K. R. Goodearl; E. S. Letzter
Journal: Trans. Amer. Math. Soc. 352 (2000), 5855-5876.
MSC (2000): Primary 16D60, 16P40, 16S36, 16W35; Secondary 20G42, 81R50
Posted: August 8, 2000
MathSciNet review: 1781280
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Abstract | References | Similar articles | Additional information

Abstract: The prime and primitive spectra of $\mathcal{O}_{\mathbf q}(k^{n})$ , the multiparameter quantized coordinate ring of affine -space over an algebraically closed field , 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 .

References:

1.: G. Abrams and J. Haefner, Primeness conditions for group graded rings, in Ring Theory, Proc. Biennial Ohio State - Denison Conf. 1992, World Scientific, Singapore, 1993, pp. 1-19. MR 96f:16050
2.: M. Artin, W. Schelter, and J. Tate, Quantum deformations of $GL_{n}$ , Communic. Pure Appl. Math. 44 (1991), 879-895. MR 92i:17014
3.: K. A. Brown and K. R. Goodearl, Prime spectra of quantum semisimple groups, Trans. Amer. Math. Soc. 348 (1996), 2465-2502. MR 96i:17007
4.: C. De Concini, V. Kac, and C. Procesi, Some remarkable degenerations of quantum groups, Comm. Math. Phys. 157 (1993), 405-427. MR 94i:17019
5.: A. W. Goldie and G. O. Michler, Ore extensions and polycyclic group rings, J. London Math. Soc. (2) 9 (1974), 337-345. MR 50:9968
6.: K. R. Goodearl and E. S. Letzter, Prime and primitive spectra of multiparameter quantum affine spaces, in Trends in Ring Theory. Proc. Miskolc Conf. 1996 (V. Dlab and L. Márki, eds.), Canad. Math. Soc. Conf. Proc. Series 22 Amer. Math. Soc., Providence, RI, 1998, pp. 39-58. MR 99h:16045
7.: K. R. Goodearl and R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, London Math. Soc. Student Texts 16, Cambridge Univ. Press, Cambridge, 1989. MR 91c:16001
8.: T. J. Hodges and T. Levasseur, Primitive ideals of ${\mathbf{C}}_{q}[SL(3)]$ , Commun. Math. Phys. 156 (1993), 581-605. MR 94k:17023
9.: -, Primitive ideals of ${\mathbf{C}}_{q}[SL(n)]$ , J. Algebra 168 (1994), 455-468. MR 95i:16038
10.: T. J. Hodges, T. Levasseur, and M. Toro, Algebraic structure of multi-parameter quantum groups, Advances in Math. 126 (1997), 52-92. MR 98e:17023
11.: A. Joseph, On the prime and primitive spectra of the algebra of functions on a quantum group, J. Algebra 169 (1994), 441-511. MR 96b:17015
12.: -, Quantum Groups and Their Primitive Ideals, Ergebnisse der Math. (3) 29, Springer-Verlag, Berlin, 1995. MR 96d:17015
13.: J. C. McConnell and J. J. Pettit, Crossed products and multiplicative analogs of Weyl algebras, J. London Math. Soc. (2) 38 (1988), 47-55. MR 90c:16011
14.: D. G. Northcott, Affine Sets and Affine Groups, London Math. Soc. Lecture Note Series 39, Cambridge Univ. Press, Cambridge, 1980. MR 82c:14002
15.: M. Vancliff, Primitive and Poisson spectra of twists of polynomial rings, Algebras and Representation Theory 2 (1999), 269-285. CMP 2000:02

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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: 10.1090/S0002-9947-00-02639-8
PII: S 0002-9947(00)02639-8
Received by editor(s): April 22, 1999
Posted: 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.
Copyright of article: Copyright 2000, American Mathematical Society

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