Automorphisms of central extensions of type I von Neumann algebras

Sergio Albeverio, et al. "Automorphisms of central extensions of type I von Neumann algebras." Studia Mathematica 207.1 (2011): 1-17. <http://eudml.org/doc/285488>.

@article{SergioAlbeverio2011,
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 $T = T_\{a\} ∘ T_\{ϕ\}$, where $T_\{a\}(x) = axa^\{-1\}$ is an inner automorphism implemented by an element a ∈ E(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.},
author = {Sergio Albeverio, Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov},
journal = {Studia Mathematica},
keywords = {von Neumann algebras; central extensions; automorphism; inner automorphism},
language = {eng},
number = {1},
pages = {1-17},
title = {Automorphisms of central extensions of type I von Neumann algebras},
url = {http://eudml.org/doc/285488},
volume = {207},
year = {2011},
}

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
VL - 207
IS - 1
SP - 1
EP - 17
AB - 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 $T = T_{a} ∘ T_{ϕ}$, where $T_{a}(x) = axa^{-1}$ is an inner automorphism implemented by an element a ∈ E(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.
LA - eng
KW - von Neumann algebras; central extensions; automorphism; inner automorphism
UR - http://eudml.org/doc/285488
ER -