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TITLE On dualities of actions and inclusions
KIAS AUTHORS Lee, Hyun Ho
JOURNAL JOURNAL OF FUNCTIONAL ANALYSIS, 2019
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ABSTRACT Following the results known in the case of a finite abelian group action on C*-algebras we prove the following two theorems; an inclusion P subset of A of (Watatani) index-finite type has the Rokhlin property (is approximately representable) if and only if the dual inclusion is approximately representable (has the Rokhlin property). an inclusion P subset of A of (Watatani) index-finite type has the tracial Rokhlin property (is tracially approximately representable) if and only if the dual inclusion is tracially approximately representable (has the tracial Rokhlin property). Moreover, we provide an alternate proof of Phillips' theorem about the relations between tracial Rokhlin action and tracially approximate representable dual action using a new conceptual framework suggested by authors. (C) 2018 Elsevier Inc. All rights reserved.
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