1Institut für Angewandte Mathematik and HCM Rheinische Friedrich-Wilhelms-Universität Bonn 53115 Bonn, Germany 2Institute of Mathematics and Information Technologies Uzbekistan Academy of Sciences 100125 Tashkent, Uzbekistan and Abdus Salam International Centre for Theoretical Physics (ICTP) Trieste, Italy 3Karakalpak State University 230113 Nukus, Uzbekistan
Studia Mathematica, Tome 207 (2011) no. 1, pp. 1-17
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 $T=T_a\circ T_\phi ,$ where $T_a(x)=axa^{-1}$ is an inner automorphism implemented by an element $a\in E(M),$ and $T_\phi $ is a special automorphism generated by an automorphism $\phi $ of the center of $E(M).$ In particular if $M$ is of type I$_\infty $ then every band preserving automorphism of $E(M)$ is inner.
Keywords:
given von neumann algebra consider its central extension type von neumann algebras coincides algebra locally measurable operators affiliated arbitrary automorphism decomposed circ phi where axa inner automorphism implemented element phi special automorphism generated automorphism phi center particular type infty every band preserving automorphism inner
1
Institut für Angewandte Mathematik and HCM Rheinische Friedrich-Wilhelms-Universität Bonn 53115 Bonn, Germany
2
Institute of Mathematics and Information Technologies Uzbekistan Academy of Sciences 100125 Tashkent, Uzbekistan and Abdus Salam International Centre for Theoretical Physics (ICTP) Trieste, Italy
3
Karakalpak State University 230113 Nukus, Uzbekistan
@article{10_4064_sm207_1_1,
author = {Sergio Albeverio and Shavkat Ayupov and Karimbergen Kudaybergenov and Rauaj Djumamuratov},
title = {Automorphisms of central extensions of
type {I} von {Neumann} algebras},
journal = {Studia Mathematica},
pages = {1--17},
year = {2011},
volume = {207},
number = {1},
doi = {10.4064/sm207-1-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm207-1-1/}
}
TY - JOUR
AU - Sergio Albeverio
AU - Shavkat Ayupov
AU - Karimbergen Kudaybergenov
AU - Rauaj Djumamuratov
TI - Automorphisms of central extensions of
type I von Neumann algebras
JO - Studia Mathematica
PY - 2011
SP - 1
EP - 17
VL - 207
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm207-1-1/
DO - 10.4064/sm207-1-1
LA - en
ID - 10_4064_sm207_1_1
ER -
%0 Journal Article
%A Sergio Albeverio
%A Shavkat Ayupov
%A Karimbergen Kudaybergenov
%A Rauaj Djumamuratov
%T Automorphisms of central extensions of
type I von Neumann algebras
%J Studia Mathematica
%D 2011
%P 1-17
%V 207
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm207-1-1/
%R 10.4064/sm207-1-1
%G en
%F 10_4064_sm207_1_1
Sergio Albeverio; Shavkat Ayupov; Karimbergen Kudaybergenov; Rauaj Djumamuratov. Automorphisms of central extensions of
type I von Neumann algebras. Studia Mathematica, Tome 207 (2011) no. 1, pp. 1-17. doi: 10.4064/sm207-1-1
