Abstract
A Hom-structure on a Lie algebra [Formula: see text] is a linear map [Formula: see text] which satisfies the Hom–Jacobi identity [Formula: see text] for all [Formula: see text]. A Hom-structure is called regular if [Formula: see text] is also a Lie algebra isomorphism. Let [Formula: see text] be the Lie algebra consisting of all strictly upper triangular [Formula: see text] matrices over a field [Formula: see text]. In this paper, we prove that if [Formula: see text], any regular Hom-structure [Formula: see text] on [Formula: see text] is a product of a special inner automorphism, an extremal inner automorphism and a central automorphism of [Formula: see text]. As its application, the set of all regular Hom-structures on [Formula: see text] forms a normal subgroup of the automorphism group of [Formula: see text].
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