English

An integration of Lie-Leibniz triples

Differential Geometry 2026-05-04 v3 Mathematical Physics math.MP Rings and Algebras

Abstract

In this paper, we introduce the group version of a Lie-Leibniz triple, which we call a Lie group-rack triple. We define a Lie group-rack triple whose tangent structure is a Lie-Leibniz triple, which is a generalization of an augmented Lie rack whose tangent structure is an augmented Leibniz algebra. We show that any finite-dimensional Lie-Leibniz triple can be integrated to a local Lie group-rack triple by generalizing the integration procedure of an augmented Leibniz algebra into an augmented Lie rack.

Keywords

Cite

@article{arxiv.2508.19143,
  title  = {An integration of Lie-Leibniz triples},
  author = {Ryo Hayami},
  journal= {arXiv preprint arXiv:2508.19143},
  year   = {2026}
}

Comments

14 pages, Some typos are corrected