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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Defending the negated Kaplansky conjecture
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by Akira Masuoka PDF
Proc. Amer. Math. Soc. 129 (2001), 3185-3192 Request permission

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
  • MR Author ID: 261525
  • Email: akira@math.tsukuba.ac.jp
  • 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
  • © Copyright 2001 American Mathematical Society
  • 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
  • MathSciNet review: 1844991