Triple derivations on von Neumann algebras

Robert Pluta¹ ; Bernard Russo²

¹ Department of Mathematics University of Iowa Iowa City, IA 52242-1419, U.S.A.
² Department of Mathematics University of California Irvine, CA 92697-3875, U.S.A.

Studia Mathematica, Tome 226 (2015) no. 1, pp. 57-73

Résumé

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.

Détail

DOI : 10.4064/sm226-1-3

Mots-clés : known every derivation von neumann algebra itself inner derivation every derivation von neumann algebra its predual inner known every triple derivation defined below von neumann algebra itself inner triple derivation examine what extent triple derivations von neumann algebra its predual inner rarely happens comes close prove triple cohomological characterization finite factors zero one law factors