Linear maps on von Neumann algebras acting as Lie type derivation via local actions

Let N be a factor von Neumann algebra with dim > 1 that operates on a Hilbert space. Within the manuscript, we let out the characterization of Lie type derivation on factor von Neumann algebra of zero product as well as at projection product and notice that it has standard form.

Automated summary

The manuscript provides a detailed characterization of Lie type derivation on factor von Neumann algebra of zero product and projection product, revealing that they have a standard form.