Non-trivial derivations on commutative regular algebras.

Título inglés	Non-trivial derivations on commutative regular algebras.
Título español	Derivaciones no triviales en álgebras regulares conmutativas.
Autor/es	Ber, A. F. ; Chilin, Vladimir I. ; Sukochev, Fyodor A.
Organización	Dep. Math. Nat. Univ. Uzbekistan, Tashkent, Uzbekistán;Sch. Informat. Eng. Flinders Univ., Bedford Park, Australia
Revista	0213-8743
Publicación	2006, 21 (2): 107-147, 20 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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.
Clasificación UNESCO	120201
Palabras clave español	Algebra de operadores ; C*-álgebras ; Algebras conmutativas ; Algebras regulares ; Algebra de Von Neumann
Código MathReviews	MR2292743
Código Z-Math	Zbl pre05174073
Acceso al artículo completo