On Lie n-centralizers, n-commuting linear maps and related mappings

TL;DR

This paper investigates linear mappings on algebras that behave like Lie n-centralizers and n-commuting maps under certain local conditions, expanding understanding of their structure and properties.

Contribution

It introduces new local conditions characterizing Lie n-centralizers and explores their relation to n-commuting linear maps, providing novel insights into their behavior.

Findings

Characterization of Lie n-centralizers under local conditions

Relationship between Lie n-centralizers and n-commuting linear maps

New criteria for identifying these mappings in algebraic structures

Abstract

In this article, we consider several local conditions under which linear mappings on algebras act like Lie n-centralizers and we study these linear mappings, Lie n-centralizers and n-commuting linear maps.