Non-trivial derivations on commutative regular algebras.

Ber, A. F., Chilin, Vladimir I., and Sukochev, Fyodor A.. "Non-trivial derivations on commutative regular algebras.." Extracta Mathematicae 21.2 (2006): 107-147. <http://eudml.org/doc/41854>.

@article{Ber2006,
abstract = {Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all Lebesgue measurable functions on [0,1], our results imply that the first (Hochschild) cohomology group H1(S[0,1], S[0,1]) is non-trivial.},
author = {Ber, A. F., Chilin, Vladimir I., Sukochev, Fyodor A.},
journal = {Extracta Mathematicae},
keywords = {Algebra de operadores; C*-álgebras; Algebras conmutativas; Algebras regulares; Algebra de Von Neumann; nontrivial derivation; commutative regular algebra operator algebra; measurable operator},
language = {eng},
number = {2},
pages = {107-147},
title = {Non-trivial derivations on commutative regular algebras.},
url = {http://eudml.org/doc/41854},
volume = {21},
year = {2006},
}

TY - JOUR
AU - Ber, A. F.
AU - Chilin, Vladimir I.
AU - Sukochev, Fyodor A.
TI - Non-trivial derivations on commutative regular algebras.
JO - Extracta Mathematicae
PY - 2006
VL - 21
IS - 2
SP - 107
EP - 147
AB - Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all Lebesgue measurable functions on [0,1], our results imply that the first (Hochschild) cohomology group H1(S[0,1], S[0,1]) is non-trivial.
LA - eng
KW - Algebra de operadores; C*-álgebras; Algebras conmutativas; Algebras regulares; Algebra de Von Neumann; nontrivial derivation; commutative regular algebra operator algebra; measurable operator
UR - http://eudml.org/doc/41854
ER -