Non-trivial derivations on commutative regular algebras

Autores: A. F. Ber, V. I. Chilin, F. A. Sukochev
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 21, Nº 2, 2006, págs. 107-148
Idioma: inglés
Títulos paralelos:
- Derivaciones no triviales en álgebras regulares conmutativas
Enlaces
- Texto completo 1 2 (pdf)
Resumen
- 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.