2-Local Lie derivations on semi-finite factor von Neumann algebras

Abstract

Let be a semi-finite von Neumann algebra factor with dimension greater than 4. We prove that every 2-local Lie derivation of can be written in the form for all , where T is an element in , and is a homogeneous map satisfying for every and every commutator .

Keywords:

• derivations
• 2-local Lie derivations
• factor von Neumann algebras

AMS Subject Classifications:

• Primary: 47B47
• Secondary: 47L10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 11401452] and China Postdoctoral Science Foundation.