Abstract

Abstract The aim of this paper is to transfer the restrictedness theory to Hom-Lie algebras. The concept of restricted Hom-Lie algebras, which is introduced in [S. Bouarroudj and A. Makhlouf, Hom-lie superalgebras in characteristic 2, Mathematics 11 2023, 24, Paper No. 4955], will be used in this paper. First, the existence and uniqueness of p-structures on a Hom-Lie algebra is studied. Then the definition of a restrictable Hom-Lie algebra is given and the equivalence relation between restrictable Hom-Lie algebras and restricted Hom-Lie algebras is constructed. Finally, the p-envelopes of a Hom-Lie algebra are defined and studied.

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