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Representations of skew polynomial algebras

Author(s): Søren Jøndrup
Journal: Proc. Amer. Math. Soc. 128 (2000), 1301-1305.
MSC (1991): Primary 16S35; Secondary 16R20
Posted: August 3, 1999
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Abstract: C. De Concini and C. Procesi have proved that in many cases the degree of a skew polynomial algebra is the same as the degree of the corresponding quasi polynomial algebra. We prove a slightly more general result. In fact we show that in case the skew polynomial algebra is a P.I. algebra, then its degree is the degree of the quasi polynomial algebra.

Our argument is then applied to determine the degree of some algebras given by generators and relations.

References:

1.: C. De Concini and C. Procesi, Quantum groups in ``Lecture Notes in Mathematics'', Vol. 1565, pp. 31-140. Springer Verlag, New York/Berlin (1993). MR 95j:17012
2.: K.R. Goodearl, Prime ideals in Skew Polynomial Rings and Quantized Weyl Algebras, J. Algebra 150 (1992), 324-377. MR 93h:16051
3.: H. P. Jakobsen and H. Zhang, The Center of a Quantized Matrix Algebra, J. Algebra 196 (1997), 458-474. MR 98i:17016
4.: H.P. Jakobsen and H. Zhang, The Center of the Dipper Donkin Quantized Matrix Algebra, Beiträge zur Algebra und Geometrie 38 (2), 411-421, 1997. MR 98i:16025
5.: S. Jøndrup, Representations of some P.I. algebras, Preprint.
6.: J. C. McConnell and J.C. Robson, Non Commutative Noetherian Rings, Wiley, Interscience, New York, 1987. MR 89j:16023


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