Asymptotic algebra and outer conjugacy classes of automorphisms of factors

This paper studies the questions of the factorization and outer conjugacy of automorphisms of factors. A decomposition of automorphisms of factors into the tensor product of two factors, one of which is the standard automorphism of the Powers factor $R_\lambda$ ($0<\lambda<1$), is given. Complete systems of invariants for outer conjugacy aperiodic automorphisms of factors of type III$_0$ are found, emerging as crossed products of a factor $R_\lambda$ with discrete subgroups of its group of modular automorphisms. Examples of factors of type III with a number of new properties are constructed.
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