Primitivity of Noetherian down-up algebras

Communications in Algebra

Volumn 28, Issue 6, 2000, Pages 2983-2997

  Kirkman, Ellen ^a   Kuzmanovich, James ^a  

^a WAKE FOREST UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034340790     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927870008827004     Document Type: Article

References (16)

1. M. Artin, Algebra, Prentice-Hall, Englewood Cliffs, 1991.
2. V. V. Bavula, Generalized Weyl algebras and their representations, St. Petersburg Math. J. 4 (1993), 71-92.
3. 2, in Recent Progress in Algebra, edited by S.G. Hahn, H.C. Myung, and E. Zelmanov, Contemporary Mathematics 224, American Mathematical Society, Providence, RI (1998).
4. G. Benkart and T. Roby, Down-up algebras, J. Algebra 209 (1998), 305-344.
5. P. A. A. B. Carvalho and I. M. Musson, Down-up algebras and their representation theory, preprint.
6. J. Dixmier, Enveloping Algebras, American Mathematical Society, Providence, 1996.
7. D. A. Jordan, Primitivity in skew Laurent polynomial rings and related rings, Math. Zeit. 213 (1993), 352-371.
8. D. A. Jordan, Down-up algebras and ambiskew polynomial rings, preprint.
9. R. S. Kulkarni, Down-up algebras and their representations, preprint.
10. E. Kirkman, I. M. Musson and D. S. Passman, Noetherian down-up algebras, Proc. Amer. Math. Soc. 127 (1999), 3161-3167.
11. A. I. Ooms, On Lie algebras with primitive envelopes, Supplements, Proc. Amer. Math. Soc. 58 (1976), 67-72.
12. J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, John Wiley and Sons, New York, 1987.
13. A. L. Rosenberg, Noncommutative Algebraic Geometry and Representations of Quantized Algebras, Kluwer, Dordrecht, 1995.
14. E. Witten, Gauge theories, vertex models, and quantum groups, Nuclear Phys. B 330 (1990), 285-346.
15. E. Witten, Quantization of Chern-Simons gauge theory with complex gauge group, Comm. Math. Phys. 137 (1991), 29-66.
16. K. Zhao, Centers of down-up algebras, preprint.