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Down-up algebras at roots of unity
Author(s):
Rajesh
S.
Kulkarni
Journal:
Proc. Amer. Math. Soc.
136
(2008),
3375-3382.
MSC (2000):
Primary 16H05;
Secondary 17B37
Posted:
May 28, 2008
MathSciNet review:
2415018
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Abstract:
In this note, we show that down-up algebras at roots of unity are maximal orders over their centers.
References:
-
- 1.
- Auslander, M., and Goldman, O., Maximal orders, Trans. Amer. Math. Soc. 97 (1960) 1-24. MR 0117252 (22:8034)
- 2.
- Benkart, G., and Roby, T., Down-up algebras, J. Algebra 209 (1998) 305-344. MR 1652138 (2000e:06001a)
- 3.
- Benkart, G., and Witherspoon, S., A Hopf structure for down-up algebras, Math. Z. 238 (2001) 523-553. MR 1869697 (2002k:16059)
- 4.
- Harada, M., Hereditary orders, Trans. Amer. Math. Soc. 107 (1963) 273-290. MR 0151489 (27:1474)
- 5.
- Kirkman, E., and Musson, I., Hopf down-up algebras, J. Algebra 262 (2003) 42-53. MR 1970801 (2004c:16065)
- 6.
- Kirkman, E., Musson, I., and Passman, D., Noetherian down-up algebras, Proc. Amer. Math. Soc. 127 (1999) 3161-3167. MR 1610796 (2000b:16042)
- 7.
- Kulkarni, R. S., Down-up algebras and their representations, J. Algebra 245 (2001) 431-462. MR 1863888 (2002k:16061)
- 8.
- McConnell, J. C., and Robson, J. C., Noncommutative Noetherian Rings, John Wiley and Sons, 1987. MR 934572 (89j:16023)
- 9.
- Stafford, J. T., Auslander-regular algebras and maximal orders, J. London Math. Soc. (2) 50 (1994) 276-292. MR 1291737 (95j:16028)
- 10.
- Williamson, S., Crossed products and hereditary orders, Nagoya Math. J. 23 (1963) 103-120. MR 0163943 (29:1242)
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Additional Information:
Rajesh
S.
Kulkarni
Affiliation:
Department of Mathematics, Wells Hall, Michigan State University, East Lansing, Michigan 48824
Email:
kulkarni@math.msu.edu
DOI:
10.1090/S0002-9939-08-09547-6
PII:
S 0002-9939(08)09547-6
Received by editor(s):
July 5, 2006
Posted:
May 28, 2008
Additional Notes:
The author was partially supported by NSF grants DMS-0311850 and DMS-0603684.
Communicated by:
Martin Lorenz
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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