An integration of Lie-Leibniz triples
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913078560423936 |
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| author | Hayami, Ryo |
| author_facet | Hayami, Ryo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An integration of Lie-Leibniz triples Hayami, Ryo Differential Geometry Mathematical Physics Rings and Algebras 22A30, 17A32 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. |
| title | An integration of Lie-Leibniz triples |
| topic | Differential Geometry Mathematical Physics Rings and Algebras 22A30, 17A32 |
| url | https://arxiv.org/abs/2508.19143 |