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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Galois groups of quantum group actions and regularity of fixed-point algebras


Author: Takehiko Yamanouchi
Journal: Trans. Amer. Math. Soc. 355 (2003), 2813-2828
MSC (2000): Primary 46L65; Secondary 22D25, 46L10, 81R50
Published electronically: March 12, 2003
MathSciNet review: 1975401
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Abstract: It is shown that, for a minimal and integrable action of a locally compact quantum group on a factor, the group of automorphisms of the factor leaving the fixed-point algebra pointwise invariant is identified with the intrinsic group of the dual quantum group. It is proven also that, for such an action, the regularity of the fixed-point algebra is equivalent to the cocommutativity of the quantum group.


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Additional Information

Takehiko Yamanouchi
Affiliation: Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810 Japan
Email: yamanouc@math.sci.hokudai.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03282-3
PII: S 0002-9947(03)03282-3
Keywords: Locally compact quantum group, action, factor, regularity
Received by editor(s): June 24, 2002
Received by editor(s) in revised form: November 6, 2002
Published electronically: March 12, 2003
Dedicated: Dedicated to Professor Masamichi Takesaki on the occasion of his seventieth birthday
Article copyright: © Copyright 2003 American Mathematical Society