Automorphisms of central extensions of type I von Neumann algebras
Abstract. Given a von Neumann algebra M we consider the central exten-sion E(M) of M. For type I von Neumann algebras E(M) coincides with thealgebra LS(M) of all locally measurable operators aﬃliated with M. In thiscase we show that an arbitrary automorphism T of E(M) can be decomposedas T = T a ◦ T φ , where T a (x) = axa −1 is an inner automorphism implementedby an element a ∈ E(M), and T φ is a special automorphism generated by anautomorphism φ of the center of E(M). In particular if M is of type I ∞ thenevery band preserving automorphism of E(M) is inner. 1. IntroductionIn the series of paper [1]-[3] we have considered derivations on the algebraLS(M) of locally measurable operators aﬃliated with a von Neumann algebraM, and on various subalgebras of LS(M). A complete description of derivationshas been obtained in the case of von Neumann algebras of type I and III.A comprehensive survey of recent results concerning derivations on various al-gebras of unbounded operators aﬃliated with von Neumann algebras is presentedin [4].It is well-known that properties of derivations on algebras are strongly cor-related with properties of automorphisms of underlying algebras (see e.g. [8]).Algebraic automorphisms of C