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Defending the negated Kaplansky conjecture


Author: Akira Masuoka
Journal: Proc. Amer. Math. Soc. 129 (2001), 3185-3192
MSC (2000): Primary 16W30, 16W35
DOI: https://doi.org/10.1090/S0002-9939-01-06005-1
Published electronically: May 10, 2001
MathSciNet review: 1844991
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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 305-8571, Japan
Email: akira@math.tsukuba.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-01-06005-1
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
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

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