<P><B>Abstract</B></P> <P>Following the results known in the case of a finite abelian group action on <SUP> C ⁎ </SUP> -algebras we prove the following two theorems;<UL> <LI> an inclus...
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https://www.riss.kr/link?id=A107743134
2019
-
SCOPUS,SCIE
학술저널
602-635(34쪽)
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
<P><B>Abstract</B></P> <P>Following the results known in the case of a finite abelian group action on <SUP> C ⁎ </SUP> -algebras we prove the following two theorems;<UL> <LI> an inclus...
<P><B>Abstract</B></P> <P>Following the results known in the case of a finite abelian group action on <SUP> C ⁎ </SUP> -algebras we prove the following two theorems;<UL> <LI> an inclusion P ⊂ 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). </LI> <LI> an inclusion P ⊂ 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). </LI> </UL> 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.</P>