|
Defending the negated Kaplansky conjecture
Author(s):
Akira
Masuoka
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3185-3192.
MSC (2000):
Primary 16W30, 16W35
Posted:
May 10, 2001
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
To answer in the negative a conjecture of Kaplansky, four recent papers independently constructed four families of Hopf algebras of fixed finite dimension, each of which consisted of infinitely many isomorphism classes. We defend nevertheless the negated conjecture by proving that the Hopf algebras in each family are cocycle deformations of each other.
References:
- [AS]
- N. Andruskiewitsch and H.-J. Schneider, Lifting of quantum linear spaces and pointed Hopf algebras of order
 , J. Algebra 209 (1998), 658-691. MR 99k:16075 - [BDG]
- M. Beattie, S. Dascalescu and L. Grünenfelder, On the number of types of finite-dimensional Hopf algebras, Invent. math. 136 (1999), 1-7. MR 2000a:16068
- [D]
- Y. Doi, Braided bialgebras and quadratic bialgebras, Comm. Algebra 21 (1993), 1731-1749. MR 94a:16071
- [G]
- S. Gelaki, Pointed Hopf algebras and Kaplansky's 10th conjecture, J. Algebra 209 (1998), 635-657. MR 99j:16024
- [M]
- Eric Müller, Finite subgroups of the quantum general linear group, Proc. London Math. Soc. 81 (2000), no. 1, 190-210. CMP 2000:12
- [R]
- D. Radford, On Kauffman's knot invariants arising from finite-dimensional Hopf algebras, In: J. Bergen and S. Montgomery (eds.), ``Advances in Hopf algebras", Lec. Notes in Pure and Applied Math. Vol. 158, Dekker, New York, 1994, pp. 205-266. MR 96g:57013
- [P]
- Peter Schauenburg, Hopf bigalois extensions, Comm. Algebra 24 (1996), 3797-3825. MR 97f:16064
- [S]
- H.-J. Schneider, Some remarks on exact sequences of quantum groups, Comm. Algebra 21 (1992), 3337-3358. MR 94e:17026
- [T1]
- M. Takeuchi, Some topics on
 , J. Algebra 147 (1992), 379-410. MR 93b:17055 - [T2]
- M. Takeuchi, Cocycle deformations of coordinate rings of quantum matrices, J. Algebra 189 (1997), 23-33. MR 97m:16077
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
16W30, 16W35
Retrieve articles in all Journals with MSC
(2000):
16W30, 16W35
Additional Information:
Akira
Masuoka
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
Email:
akira@math.tsukuba.ac.jp
DOI:
10.1090/S0002-9939-01-06005-1
PII:
S 0002-9939(01)06005-1
Keywords:
Hopf algebra,
quantum group,
cocycle deformation,
monoidal Morita-Takeuchi equivalence.
Received by editor(s):
August 4, 1999
Received by editor(s) in revised form:
March 22, 2000
Posted:
May 10, 2001
Dedicated:
Dedicated to Professor Yukio Tsushima on his sixtieth birthday
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org