Representations of skew polynomial algebras

Author:
Søren Jøndrup

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1301-1305

MSC (1991):
Primary 16S35; Secondary 16R20

DOI:
https://doi.org/10.1090/S0002-9939-99-05148-5

Published electronically:
August 3, 1999

MathSciNet review:
1641638

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Abstract | References | Similar Articles | Additional Information

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.

**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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Additional Information

**Søren Jøndrup**

Affiliation:
Mathematics Institute, Universitetsparken 5, DK 2100 Copenhagen Ø, Denmark

Email:
jondrup@math.ku.dk

DOI:
https://doi.org/10.1090/S0002-9939-99-05148-5

Received by editor(s):
March 10, 1998

Received by editor(s) in revised form:
June 29, 1998

Published electronically:
August 3, 1999

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 2000
American Mathematical Society