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Triple derivations on von Neumann algebras

Volume 226 / 2015

Robert Pluta, Bernard Russo Studia Mathematica 226 (2015), 57-73 MSC: Primary 46L57, 17C65; Secondary 46L10. DOI: 10.4064/sm226-1-3

Abstract

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.

Authors

  • Robert PlutaDepartment of Mathematics
    University of Iowa
    Iowa City, IA 52242-1419, U.S.A.
    e-mail
  • Bernard RussoDepartment of Mathematics
    University of California
    Irvine, CA 92697-3875, U.S.A.
    e-mail

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