Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Completions of quantum coordinate rings

Author(s): Linhong Wang
Journal: Proc. Amer. Math. Soc. 137 (2009), 911-919.
MSC (2000): Primary 16W60, 16L30
Posted: 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 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.

References:

1.: V. I. Arnautov, S. T. Glavatsky and A.V. Mikhalev, Introduction to the Theory of Topological Rings and Modules, Pure and Applied Mathematics 197, Marcel Dekker, Inc., New York, 1996. MR 1368852 (97g:16057)
2.: M. Artin, W. Schelter, and J. Tate, Quantum deformations of , Comm. Pure Appl. Math., 44 (1991), 879-895. MR 1127037 (92i:17014)
3.: K. Brown and K. Goodearl, Lectures on Algebraic Quantum Groups, Basel: Birkhäuser, 2002. MR 1898492 (2003f:16067)
4.: G. Cauchon, Effacement des dérivations et spectres premiers des algèbres quantiques, J Alg, 260 (2003), 476-518. MR 1967309 (2004g:16044)
5.: P. M. Cohn, Skew Fields: Theory of General Division Rings, Encyclopedia of Mathematics and Its Applications 57, Cambridge University Press, Cambridge, 1995. MR 1349108 (97d:12003)
6.: K. R. Goodearl and R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, Second Edition, London Mathematical Society Student Texts 61, Cambridge University Press, Cambridge, 2004. MR 2080008 (2005b:16001)
7.: K. L. Horton, The prime and primitive spectra of multiparameter quantum symplectic and Euclidean spaces, Comm Alg, (10) 31 (2003), 4713-4743. MR 1998025 (2004f:16073)
8.: R. M. Kashaev, The Heisenberg double and the pentagon relation, Algebra i Analiz, 8 (1996), no. 4, 63-74. MR 1418255 (97j:16055)
9.: T. H. Koornwinder, Special functions and -commuting variables, Special Functions, -Series and Related Topics (Toronto, Ontario, 1995), Fields Institute Communications 14, Amer. Math. Soc., Providence, RI, 1997, 131-166. MR 1448685 (99e:33024)
10.: H. Li and F. Van Oystaeyen, Zariskian Filtrations, Kluwer Academic Publishers, Dordrecht, 1996. MR 1420862 (97m:16083)
11.: J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Graduate Studies in Mathematics, vol. 30, American Mathematical Society, Providence, RI, 2000. MR 1811901 (2001i:16039)
12.: C. Năstasescu and F. Van Oystaeyen, Graded Ring Theory, North-Holland, Amsterdam, 1982. MR 676974 (84i:16002)
13.: P. Schneider and O. Venjakob, On the codimension of modules over skew power series rings with applications to Iwasawa algebras, J. Pure Appl Algebra, 204 (2006), 349-367. MR 2184816 (2006i:16067)
14.: O. Venjakob, A non-commutative Weierstrass preparation theorem and applications to Iwasawa theory (with an appendix by Denis Vogel), J. Reine Angew Math., 559 (2003), 153-191. MR 1989649 (2004e:11123)
15.: R. Walker, Local rings and normalizing sets of elements, Proc London Math Soc, (3) 24 (1972), 27-45. MR 0294399 (45:3469)

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