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Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Then, we define a Hom-exponential ($\mathsf{Hexp}$) map from the Hom-Lie algebra of a Hom-Lie group to the Hom-Lie group and discuss the universality of this $\mathsf{Hexp}$ map. We also describe a Hom-Lie group action on a smooth manifold. Subsequently, we give the notion of an adjoint representation of a Hom-Lie group on its Hom-Lie algebra. At last, we integrate the Hom-Lie algebra $(\mathfrak{gl}(V),[\cdot,\cdot],\mathsf{Ad})$, and the derivation Hom-Lie algebra of a Hom-Lie algebra.
Keywords: Hom-Lie algebra, derivation, integration.
Mots-clés : Hom-Lie group, automorphism 
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     author = {Jun Jiang and Satyendra Kumar Mishra and Yunhe Sheng},
     title = {Hom-Lie {Algebras} and {Hom-Lie} {Groups,} {Integration} and {Differentiation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a136/}
}
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Jun Jiang; Satyendra Kumar Mishra; Yunhe Sheng. Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a136/

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