※ Zoom 회의 ID: 356 501 3138, PW: 471247

In this talk, based on a joint work with professor Osaka in Japan we present duality notions in group actions and inclusions of $$extract_itex$$Csp*$$/extract_itex$$-algebras.

More precisely we will consider the tracial Rokhlin property of finite (abelian) group action $$extract_itex$$alpha: G curvearrowright A$$/extract_itex$$ and tracially approximately representable finite abelian group action $$extract_itex$$alpha:G curvearrowright A$$/extract_itex$$ and corresponding notions in an inclusion of unital $$extract_itex$$Csp*$$/extract_itex$$-algebras. Duality between group actions is due to M. Izumi in the strict case and N. C. Phillips in the tracial case. Our result is about the analogous results in the setting of inclusions. We also consider a popular trend in the stuncture theory of $$extract_itex$$Csp*$$/extract_itex$$-algebras, a transition from projections to positive elements and suggest how to modify aforementioned notions.