Automorphisms of central extensions of
type I von Neumann algebras
Studia Mathematica, Tome 207 (2011) no. 1, pp. 1-17
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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
Affiliations des auteurs :
Sergio Albeverio 1 ; Shavkat Ayupov 2 ; Karimbergen Kudaybergenov 3 ; Rauaj Djumamuratov 3
@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/}
}
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%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
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