Defending the negated Kaplansky conjecture
Author:
Akira Masuoka
Journal:
Proc. Amer. Math. Soc. 129 (2001), 31853192
MSC (2000):
Primary 16W30, 16W35
Published electronically:
May 10, 2001
MathSciNet review:
1844991
Fulltext PDF Free Access
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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.
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Additional Information
Akira Masuoka
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 3058571, Japan
Email:
akira@math.tsukuba.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993901060051
PII:
S 00029939(01)060051
Keywords:
Hopf algebra,
quantum group,
cocycle deformation,
monoidal MoritaTakeuchi equivalence.
Received by editor(s):
August 4, 1999
Received by editor(s) in revised form:
March 22, 2000
Published electronically:
May 10, 2001
Dedicated:
Dedicated to Professor Yukio Tsushima on his sixtieth birthday
Communicated by:
Ken Goodearl
Article copyright:
© Copyright 2001 American Mathematical Society
