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arXiv · 1904.06515

Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation

Jun Jiang·Satyendra Kumar Mishra·Yunhe Sheng
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Abstract

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 $(\mathfrak{gl}(V),[\cdot,\cdot],\mathsf{Ad})$, and the derivation Hom-Lie algebra of a Hom-Lie algebra.

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BibTeXRIS

Jun Jiang, Satyendra Kumar Mishra, Yunhe Sheng. 2019-04-13. Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation. https://doi.org/10.3842/sigma.2020.137

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