Skip to main navigation Skip to search Skip to main content

Automorphisms of central extensions of type I von Neumann algebras

  • University of Bonn
  • Karakalpak State University
  • Academy of Sciences of the Republic of Uzbekistan
  • Abdus Salam International Centre for Theoretical Physics

Research output: Contribution to journalArticlepeer-review

Abstract

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 = Ta ο Tφ where Ta(x) = axa-1 is an inner automorphism implemented by an element a 2 ∈ (M), and T φ is a special automorphism generated by an automorphism φ of the center of E(M): In particular if M is of type I then every band preserving automorphism of E(M) is inner.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalStudia Mathematica
Volume207
Issue number1
DOIs
StatePublished - 2011
Externally publishedYes

Fingerprint

Dive into the research topics of 'Automorphisms of central extensions of type I von Neumann algebras'. Together they form a unique fingerprint.

Cite this