Triple derivations on von Neumann algebras

Robert Pluta, and Bernard Russo. "Triple derivations on von Neumann algebras." Studia Mathematica 226.1 (2015): 57-73. <http://eudml.org/doc/285461>.

@article{RobertPluta2015,
abstract = { It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its predual are inner. This rarely happens but it comes close. We prove a (triple) cohomological characterization of finite factors and a zero-one law for factors. },
author = {Robert Pluta, Bernard Russo},
journal = {Studia Mathematica},
keywords = {triple derivation; ternary weak amenability; von Neumann factor; commutator},
language = {eng},
number = {1},
pages = {57-73},
title = {Triple derivations on von Neumann algebras},
url = {http://eudml.org/doc/285461},
volume = {226},
year = {2015},
}

TY - JOUR
AU - Robert Pluta
AU - Bernard Russo
TI - Triple derivations on von Neumann algebras
JO - Studia Mathematica
PY - 2015
VL - 226
IS - 1
SP - 57
EP - 73
AB - It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its predual are inner. This rarely happens but it comes close. We prove a (triple) cohomological characterization of finite factors and a zero-one law for factors.
LA - eng
KW - triple derivation; ternary weak amenability; von Neumann factor; commutator
UR - http://eudml.org/doc/285461
ER -