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I am interested in understanding Morita equivalence of $Z_2$-graded von Neumann algebras. In the ungraded case, Rieffel showed that all Type I factors are Morita-equivalent, while for Type III factors Morita-equivalence is the same as isomorphism. I would like to know the graded version of these results. In the graded case it is natural to define a factor as a von Neumann algebra whose super-center consists of scalars. It would also be interesting to know a G-equivariant version, where G is a finite group.

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