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On pointed Hopf algebras of dimension
Author(s):
M.
Beattie;
S.
Dascalescu;
L.
Grünenfelder
Journal:
Proc. Amer. Math. Soc.
128
(2000),
361-367.
MSC (1991):
Primary 16W30
Posted:
July 6, 1999
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Abstract:
In this note we describe nonsemisimple Hopf algebras of dimension with coradical isomorphic to , abelian of order , over an algebraically closed field of characteristic zero. If is cyclic or , then we also determine the number of isomorphism classes of such Hopf algebras.
References:
- 1.
- N. Andruskiewitsch and H.-J. Schneider, Hopf algebras of order
and braided Hopf algebras of order , J. Algebra 199 (1998), 430-454. CMP 98:06 - 2.
- M. Beattie, S. D\u{a}sc\u{a}lescu, L. Grünenfelder, C. N\u{a}st\u{a}sescu, Finiteness conditions, co-Frobenius Hopf algebras and quantum groups, J. Algebra 200 (1998), 312-333. CMP 98:08
- 3.
- M. Beattie, S. D\u{a}sc\u{a}lescu, L. Grünenfelder, Constructing pointed Hopf algebras by Ore extensions, preprint.
- 4.
- S. Gelaki, Quantum groups of dimension
, Israel J. Math. 102 (1997), 227-267. CMP 98:06 - 5.
- S. Gelaki, On Pointed Ribbon Hopf Algebras, J. Algebra 181 (1996), 760-786. MR 97d:16044
- 6.
- C. Kassel, Quantum Groups, Graduate Texts in Mathematics 155 (1995), Springer Verlag. MR 96e:17041
- 7.
- R. Larson and D. Radford, Semisimple Hopf algebras, J. Algebra 171 (1995), 5-35. MR 96a:16040
- 8.
- A. Masuoka, Semisimple Hopf algebras of dimension 6,8, Israel J. Math. 92 (1995), 361-373. MR 96j:16045
- 9.
- A. Masuoka, Self-dual Hopf algebras of dimension
obtained by extension, J. Algebra 178 (1995), 791-806. MR 96j:16046 - 10.
- A. Masuoka, The
theorem for semisimple Hopf algebras, Proc. Amer. Math. Soc. 124 (1996), 735-737. MR 96f:16046 - 11.
- A. Masuoka, Semisimple Hopf algebras of dimension
, Comm. Algebra 23 (1995), 1931-1940. MR 96e:16050 - 12.
- S. Montgomery, Hopf algebras and their actions on rings, CBMS no. 82, Amer. Math. Soc., 1993. MR 94i:16019
- 13.
- D. E. Radford, Operators on Hopf algebras, Amer. J. Math. 99 (1977), 139-158. MR 55:10505
- 14.
- D. E. Radford, Irreducible representations of
arising from Mod , Israel Math. Conference Proceedings 7 (1993), 143-170. MR 95b:17020 - 15.
- D. E. Radford, On Kauffman's knot invariants arising from finite-dimensional Hopf algebras, in ``Advances in Hopf Algebras", Lecture Notes in Pure and Appl. Math., vol. 158, 205-266, Marcel Dekker, New York, 1994. MR 96g:57013
- 16.
- D. Stefan, Hopf subalgebras of pointed Hopf algebras and applications, Proc. Amer. Math. Soc. 125 (1997), 3191-3193. MR 97m:16076
- 17.
- Y. Zhu, Hopf algebras of prime dimension, Int. Math. Research Notices 1 (1994), 53-59. MR 94j:16072
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Additional Information:
M.
Beattie
Affiliation:
Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada E4L 1E6
Email:
mbeattie@mta.ca
S.
Dascalescu
Affiliation:
Faculty of Mathematics, University of Bucharest, Str. Academiei 14, RO-70109 Bucharest 1, Romania
Email:
sdascal@al.math.unibuc.ro
L.
Grünenfelder
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Email:
Luzius@mscs.dal.ca
DOI:
10.1090/S0002-9939-99-04996-5
PII:
S 0002-9939(99)04996-5
Received by editor(s):
October 7, 1997
Received by editor(s) in revised form:
April 3, 1998
Posted:
July 6, 1999
Additional Notes:
The first and third authors research was partially supported by NSERC
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1999,
American Mathematical Society
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