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Description of the Automorphism Group Aut(A/Aα) for a Minimal Action of a Compact Kac Algebra and Its Application

✍ Scribed by Takehiko Yamanouchi

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
199 KB
Volume
194
Category
Article
ISSN
0022-1236

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✦ Synopsis

It is shown that, for a minimal action a of a compact Kac algebra K on a factor A, the group of all automorphisms leaving the fixed-point algebra A a pointwise invariant is topologically isomorphic to the intrinsic group of the dual Kac algebra # K K. As an application, in the case where dim K o 1, the left (in fact, two-sided) coideal of K determined by the normalizer (group) of A a in A through the Izumi-Longo-Popa (Galois) correspondence is identified. As a consequence, we prove that, when A is the AFD II 1 factor, K is cocommutative if and only if A a A contains a common Cartan subalgebra. This result is an extension of a result due to Jones and Popa.

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