What question did this study set out to answer?

The aim is to understand the properties of nonlinear 2-local Lie centralizers in von Neumann algebras without central summands.

June 14, 2026

Nonlinear 2-local Lie n -centralizers of von Neumann algebras

Key Points

The aim is to understand the properties of nonlinear 2-local Lie centralizers in von Neumann algebras without central summands.
Defined the concept of nonlinear 2-local Lie centralizers within von Neumann algebras.
Analyzed the relationships between centralizers and annihilating mappings of commutators.
Proved that if a nonlinear 2-local Lie centralizer exists, certain commutators are annihilated by a specific mapping.

Abstract

Let Formula: see text be a finite von Neumann algebra with no central summands of type Formula: see text. If Formula: see text is a nonlinear 2-local Lie Formula: see text-centralizer with Formula: see text, then Formula: see text for all Formula: see text, where Formula: see text and Formula: see text is a mapping which annihilates each Formula: see text-th commutator of Formula: see text.

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