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Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
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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 (Hexp) map from the Hom-Lie algebra of a Hom-Lie group to the Hom-Lie group and discuss the universality of this 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 (gl(V),[.,.],Ad), and the derivation Hom-Lie algebra of a Hom-Lie algebra.
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Title: Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Description:
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 (Hexp) map from the Hom-Lie algebra of a Hom-Lie group to the Hom-Lie group and discuss the universality of this 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 (gl(V),[.
,.
],Ad), and the derivation Hom-Lie algebra of a Hom-Lie algebra.
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