Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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.
Jiang, Jun; Mishra, Satyendra Kumar; and Sheng, Yunhe, "Hom-lie algebras and hom-lie groups, integration and differentiation" (2020). Journal Articles. 455.