Automorphisms of central extensions of type I von Neumann algebras

作者：Albeverio Sergio^*; Ayupov Shavkat; Kudaybergenov Karimbergen; Djumamuratov Rauaj

来源：Studia Mathematica, 2011, 207(1): 1-17.

DOI：10.4064/sm207-1-1

• von Neumann algebras
• central extensions
• automorphism
• inner automorphism

Given a von Neumann algebra M we consider its central extension E(M). For type I von Neumann algebras, E(M) coincides with the algebra LS(M) of all locally measurable operators affiliated with M. In this case we show that an arbitrary automorphism T of E(M) can be decomposed as T = T-a circle T phi, where T-a(x) = axa(-1) is an inner automorphisrn implemented by an element a is an element of E(M), and T-phi is a special automorphism generated by an automorphism phi of the center of E(M). In particular if Al is of type I-infinity then every band preserving automorphism of E(M) is inner.

• 出版日期2011