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Proceedings of the American Mathematical Society

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Completions of quantum coordinate rings


Author: Linhong Wang
Journal: Proc. Amer. Math. Soc. 137 (2009), 911-919
MSC (2000): Primary 16W60, 16L30
DOI: https://doi.org/10.1090/S0002-9939-08-09620-2
Published electronically: October 16, 2008
MathSciNet review: 2457430
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Abstract: Given an iterated skew polynomial ring $ C[y_1;\tau_1,\delta_1]\ldots [y_n;\tau_n,\delta_n]$ over a complete local ring $ C$ with maximal ideal $ \mathfrak{m}$, we prove, under suitable assumptions, that the completion at the ideal $ \mathfrak{m} + \left\langle y_1,y_2,\ldots,y_n\right\rangle$ is an iterated skew power series ring. Under further conditions, the completion becomes a local, noetherian, Auslander regular domain. Applicable examples include quantum matrices, quantum symplectic spaces, and quantum Euclidean spaces.


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Additional Information

Linhong Wang
Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122-6094
Address at time of publication: Department of Mathematics, Southeastern Louisiana University, SLU 10687, Hammond, Louisiana 70402
Email: lwang@selu.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09620-2
Received by editor(s): November 9, 2007
Received by editor(s) in revised form: March 26, 2008
Published electronically: October 16, 2008
Communicated by: Birge Huisgen-Zimmermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.