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A Twisted Generalization of Lie-Yamaguti Algebras

Abstract : A twisted generalization of Lie-Yamaguti algebras, called Hom-Lie-Yamaguti algebras, is defined. Hom-Lie-Yamaguti algebras generalize multiplicative Hom-Lie triple systems (and subsequently ternary mul- tiplicative Hom-Nambu algebras) and Hom-Lie algebras in the same way as Lie-Yamaguti algebras generalize Lie triple systems and Lie algebras. It is shown that the category of (multiplicative) Hom-Lie- Yamaguti algebras is closed under twisting by self-morphisms. Con- structions of Hom-Lie-Yamaguti algebras from ordinary Lie-Yamaguti algebras and Malcev algebras are given. Using the well-known classifi- cation of real two-dimensional Lie-Yamaguti algebras, examples of real two-dimensional Hom-Lie-Yamaguti algebras are given.
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Donatien Gaparayi, Issa A. Nourou. A Twisted Generalization of Lie-Yamaguti Algebras. International Journal of Algebra, 2012, Vol. 6 (no. 7), pp.339 - 352. ⟨hal-00962371⟩

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