|
On the Projectivity of module coalgebras
Author(s):
Siu-Hung
Ng
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3191-3198.
MSC (1991):
Primary 16W30
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we derive some criteria for the projectivity of a module coalgebra over a finite dimensional Hopf algebra. In particular, we show that any Hopf algebra over a field of characteristic zero is faithfully flat over its group-like subHopf algebra. Finally, we prove that if  is a finite dimensional subHopf algebra of a Hopf algebra  , then  is normal in  if and only if  . This improves a result by S. Montgomery (1993).
References:
- 1.
- C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras (Interscience, New York, 1962). MR 90g:16001
- 2.
- Y. Doi, On the structure of relative Hopf modules, Comm. Algebra 11 (1983), 243-255. MR 84a:16014
- 3.
- I. Kaplansky, Bialgebras, Chicago Press, 1975. MR 55:8087
- 4.
- S. Montgomery, Hopf algebras and their actions on rings, CBMS Lecture Notes, vol. 82, Amer. Math. Soc., Providence, RI, 1993. MR 94i:16019
- 5.
- W. D. Nichols and M. B. Zoeller, A Hopf algebra freeness theorem, Amer. J. Math. 111 (1989), 381-385. MR 90c:16008
- 6.
- D. E. Radford, Freeness (projectivity) criteria for Hopf algebras over Hopf subalgebras, J. Pure Appl. Algebra 11 (1977) 15-28. MR 57:16344
- 7.
- H.-J. Schneider, Some remarks on exact sequences of quantum groups. Comm. Algebra 21 (1993), 3337-3357. MR 94e:17026
- 8.
- M. Sweedler, Hopf algebras, Benjamin, New York, 1969. MR 40:5705
- 9.
- M. Takeuchi, Quotient spaces for Hopf algebras. Comm. Algebra 22 (1994), 2503-2523. MR 95h:16055
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
16W30
Retrieve articles in all Journals with MSC
(1991):
16W30
Additional Information:
Siu-Hung
Ng
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Address at time of publication:
Department of Mathematics, University of California at Santa Cruz, Santa Cruz, California 95064
Email:
shng@math.ucsc.edu
DOI:
10.1090/S0002-9939-98-04599-7
PII:
S 0002-9939(98)04599-7
Received by editor(s):
September 27, 1996
Received by editor(s) in revised form:
April 3, 1997
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org