Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Differential Geometry
2021-02-09 v3
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 , and the derivation Hom-Lie algebra of a Hom-Lie algebra.
Cite
@article{arxiv.1904.06515,
title = {Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation},
author = {Jun Jiang and Satyendra Kumar Mishra and Yunhe Sheng},
journal= {arXiv preprint arXiv:1904.06515},
year = {2021}
}