# Non-trivial derivations on commutative regular algebras.

A. F. Ber; Vladimir I. Chilin; Fyodor A. Sukochev

Extracta Mathematicae (2006)

- Volume: 21, Issue: 2, page 107-147
- ISSN: 0213-8743

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topBer, 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 -