Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-19T07:26:12.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Invariants for automorphisms of certain iterated skew polynomial rings

Published online by Cambridge University Press:  20 January 2009

David A. Jordan  and
Imogen E. Wells
David A. Jordan
Affiliation:
School of Mathematics and Statistics University of Sheffield The Hicks Building Sheffield S3 7RH, UK
Imogen E. Wells
Affiliation:
School of Mathematics and Statistics University of Sheffield The Hicks Building Sheffield S3 7RH, UK
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Rings of invariants are identified for some automorphisms θ of certain iterated skew polynomial rings R, including the enveloping algebra of sl2(k), the Weyl algebra A1 and their quantizations. We investigate how finite-dimensional simple R-modules split over the ring of invariants Rθ and how finite-dimensional simple Rθ-modules extend to R.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 3 , October 1996 , pp. 461 - 472
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Bell, A. D. and Smith, S. P., Some 3-dimensional skew polynomial rings, preprint, University of Wisconsin and University of Washington.Google Scholar
2. Goodearl, K. R. and Letzter, E. S., Prime ideals in skew and q-skew polynomial rings, Mem. Amer. Math. Soc. 109 (1994), no. 521.Google Scholar
3. Jordan, D. A., Iterated skew polynomial rings and quantum groups, J. Algebra 156 (1993), 194–218.CrossRefGoogle Scholar
4. Jordan, D. A., Krull and global dimension of certain iterated skew polynomial rings. In Abelian Groups and Noncommutative Rings (a collection of papers in memory of Robert B. Warfield, Jr.), Contemp. Math. 130 (1992), 201–213.CrossRefGoogle Scholar
5. Jordan, D. A., Height one prime ideals of certain iterated skew polynomial rings, Math. Proc. Cambridge Philos. Soc. 114 (1993), 407–425.CrossRefGoogle Scholar
6. Jordan, D. A., Primitivity in skew Laurent polynomial rings and related rings, Math. Z. 213 (1993), 353–371.CrossRefGoogle Scholar
7. Jordan, D. A., Finite-dimensional simple modules over certain iterated skew polynomial rings, J. Pure Appl. Algebra 98 (1995), 45–55.CrossRefGoogle Scholar
8. Kraft, H. and Small, L., Invariant algebras and completely reducible representations, Mathematical Research Letters 1 (1994), 297–307.CrossRefGoogle Scholar
9. Passman, D. S., Infinite crossed products (Academic Press, San Diego, London, 1989).Google Scholar
10. Smith, S. P., A class of algebras similar to the enveloping algebra of sl(2), Trans. Amer. Math. Soc. 322 (1990), 285–314.Google Scholar
11. Wells, I. E., Simplicity in some iterated skew polynomial rings, in preparation.Google Scholar
12. Woronowicz, S. L., Twisted SU(2)-group. An example of a non-commutative differential calculus, Publ R.M.I.S., Kyoto Univ. 23 (1987), 117–181.CrossRefGoogle Scholar