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Primitive ideals in the coordinate ring of quantum Euclidean space

Published online by Cambridge University Press:  17 April 2009

Sei-Qwon Oh
Affiliation:
Department of Mathematics, Chungnam National University, Taejon 305–764, Korea e-mail: [email protected], [email protected]
Chun-Gil Park
Affiliation:
Department of Mathematics, Chungnam National University, Taejon 305–764, Korea e-mail: [email protected], [email protected]
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Abstract

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A twisted group algebra kσP on a free Abelian group P with finite rank and a Poisson structure on kP are studied. As an application, the primitive spectrum of , the coordinate ring of quantum Euclidean space, is described and a Poisson algebra A is constructed so that there is a bijection between the primitive spectrum of and the symplectic spectrum of R.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Akhavizadegan, M. and Jordan, D.A., ‘Prime ideals of quantized Weyl algebras’ (to appear).Google Scholar
[2]Goodearl, K.R. and Lenagan, T.H., ‘Catenarity in quantum algebras’, J. Pure Appl. Algebra 111 (1996), 123142.CrossRefGoogle Scholar
[3]Goodearl, K.R. and Letzter, E.S., ‘Prime factor algebras of the coordinate ring of quantum matrices’, Proc. Amer. Math. Soc. 121 (1994), 10171025.CrossRefGoogle Scholar
[4]Jordan, D.A., ‘A simple localization of the quantized Weyl algebra’, J. Algebra 174 (1995), 267288.CrossRefGoogle Scholar
[5]Joseph, A., Quantum groups and their primitive ideals, A series of modern surveys in mathematics, (3. Folge, Band 29) (Springer-Verlag, Berlin, Heidelberg, New York, 1995).CrossRefGoogle Scholar
[6]McConnell, J.C. and Pettit, J.J., ‘Crossed products and multiplicative analogues of Weyl algebras’, J. London Math. Soc. 38 (1988), 4755.CrossRefGoogle Scholar
[7]McConnell, J.C. and Robson, J.C., Noncommutative Noetherian rings (Wiley–Interscience, New York, 1987).Google Scholar
[8]Oh, Sei-Qwon, ‘Primitive ideals of the coordinate ring of quantum symplectic space’, J. Algebra 174 (1995), 531552.CrossRefGoogle Scholar
[9]Oh, Sei-Qwon, ‘Catenarity in a class of iterated skew polynomial rings’, Comm. Algebra 25 1 (1997), 3749.CrossRefGoogle Scholar
[10]Smith, S.P., ‘Quantum groups: An introduction and survey for ring theorists’, in Noncommutative Rings, (Montgomery, S. and Small, L., Editors), M.S.R.I. Publ. 24 (Springer-Verlag, Berlin, Heidelberg, New York, 1992), pp. 131178.CrossRefGoogle Scholar
[11]Takeuchi, M., ‘Matric bialgebras and quantum groups’, Israel J. Math. 72 (1990), 232251.Google Scholar