On Hom-Lie triple systems and involutions of Hom-Lie algebras
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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.
Abstract
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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