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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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