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

Yamanouchi, Takehiko

doi:10.1090/S0002-9947-03-03282-3

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

Trans. Amer. Math. Soc. 355 (2003), 2813-2828

DOI: https://doi.org/10.1090/S0002-9947-03-03282-3

Published electronically: March 12, 2003

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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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