Article Type

Research Article

Publication Title

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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 (gl(V ), [·, ·], Ad), and the derivation Hom-Lie algebra of a Hom-Lie algebra.

DOI

10.3842/SIGMA.2020.137

Publication Date

1-1-2020

Comments

Open Access, Gold, Green

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