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In this paper we mainly establish a relationship between involutions of multiplicative Hom-Lie algebras and Hom-Lie triple systems. We show that the $-1$-eigenspace of any involution on any multiplicative Hom-Lie algebra becomes a Hom-Lie triple system and we construct some examples of Hom-Lie triple systems using some involutions of some classical Hom-Lie algebras.
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 A. Baklouti, Quadratic Hom-Lie triple systems, J. Geom. Phys. 121 (2017), 166–175. Google Scholar
 S. Benayadi and A. Makhlouf, Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms, J. Geom. Phys. 76 (2014), 38–60. Google Scholar
 E. Cartan, Oeuvres compl`etes, Part 1, vol. 2, nos. 101, 138, Paris, Gauthier-Villars, 1952. Google Scholar
 J. T. Hartwig, D. Larsson and S.D. Silvestrov, Deformations of Lie algebras unsing σ- derivations, J. Algebra. 295 (2006), 314–361. Google Scholar
 T. L. Hodge, Lie triple systems, restricted Lie triple systems and algebraic groups, J. Algebra. 244 (2001), 533–580. Google Scholar
 N. Jacobson, Lie and Jordan triple systems, Amer. J. Math. 71 (1949), 149–170. Google Scholar
 N. Jacobson, General representation theory of Jordan algebras, Trans. Amer. Math. Soc. 70 (1951), 509–548. Google Scholar
 W. G. Lister, A structure theory for Lie triple systems, Trans. Amer. Math. Soc. 72 (1952), 217–242. Google Scholar
 D. Yau, On n-ary Hom-Nambu and Hom-Nambu-Lie algebras, J. Geom. Phys. 62 (2012), 506–522. Google Scholar
 D. Yau, Hom-algebras and homology, J. Lie Theory. 19 (2009), 409–421 . Google Scholar
 J. Zhou, L. Chen and Y. Ma, Generalized derivations of Lie triple systems, Open Math. 14 (2016), 260–271. Google Scholar