Abstract
Let [Formula: see text] be the Lie algebra consisting of all strictly upper triangular [Formula: see text] matrices over a field [Formula: see text]. An invertible linear map [Formula: see text] on [Formula: see text] is called to be strong commutativity preserving (simply denoted by SCP) if [Formula: see text] for any [Formula: see text]. We show that for [Formula: see text], an invertible linear map [Formula: see text] preserves strong commutativity if and only if there exist [Formula: see text] and a linear function [Formula: see text] with [Formula: see text] such that [Formula: see text], where [Formula: see text] is an inner SCP, [Formula: see text] are extremal SCPs, [Formula: see text] is a central SCP.
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