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

 

Spectra of quantized hyperalgebras


Authors: William Chin and Leonid Krop
Journal: Trans. Amer. Math. Soc. 358 (2006), 4553-4567
MSC (2000): Primary 16W35, 16W30, 17B37, 81R50
Published electronically: April 11, 2006
MathSciNet review: 2231388
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Abstract: We describe the prime and primitive spectra for quantized enveloping algebras at roots of 1 in characteristic zero in terms of the prime spectrum of the underlying enveloping algebra. Our methods come from the theory of Hopf algebra crossed products. For primitive ideals we obtain an analogue of Duflo's Theorem, which says that every primitive ideal is the annihilator of a simple highest weight module. This depends on an extension of Lusztig's tensor product theorem.


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Additional Information

William Chin
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email: wchin@condor.depaul.edu

Leonid Krop
Affiliation: Department of Mathematics, DePaul University, Chicago, Illinois 60614
Email: lkrop@condor.depaul.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03860-8
PII: S 0002-9947(06)03860-8
Received by editor(s): November 5, 2003
Received by editor(s) in revised form: September 27, 2004
Published electronically: April 11, 2006
Additional Notes: This work was supported in part by a grant from the University Research Council of DePaul University.
Article copyright: © Copyright 2006 American Mathematical Society