Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211082 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation. Jun Jiang, Satyendra Kumar Mishra and Yunhe Sheng. SIGMA 16 (2020), 137, 22 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862643579809169408 |
|---|---|
| author | Jiang, Jun Mishra, Satyendra Kumar Sheng, Yunhe |
| author_facet | Jiang, Jun Mishra, Satyendra Kumar Sheng, Yunhe |
| citation_txt | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation. Jun Jiang, Satyendra Kumar Mishra and Yunhe Sheng. SIGMA 16 (2020), 137, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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 ((V), [⋅, ⋅], ), and the derivation Hom-Lie algebra of a Hom-Lie algebra.
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| first_indexed | 2026-03-15T08:37:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211082 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T08:37:29Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Jiang, Jun Mishra, Satyendra Kumar Sheng, Yunhe 2025-12-23T13:11:48Z 2020 Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation. Jun Jiang, Satyendra Kumar Mishra and Yunhe Sheng. SIGMA 16 (2020), 137, 22 pages 1815-0659 2020 Mathematics Subject Classification: 17B40; 17B61; 22E60; 58A32 arXiv:1904.06515 https://nasplib.isofts.kiev.ua/handle/123456789/211082 https://doi.org/10.3842/SIGMA.2020.137 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 ((V), [⋅, ⋅], ), and the derivation Hom-Lie algebra of a Hom-Lie algebra. We give our warmest thanks to the referees for their very helpful suggestions that improve the paper. Research supported by NSFC (11922110). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation Article published earlier |
| spellingShingle | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation Jiang, Jun Mishra, Satyendra Kumar Sheng, Yunhe |
| title | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation |
| title_full | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation |
| title_fullStr | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation |
| title_full_unstemmed | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation |
| title_short | Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation |
| title_sort | hom-lie algebras and hom-lie groups, integration and differentiation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211082 |
| work_keys_str_mv | AT jiangjun homliealgebrasandhomliegroupsintegrationanddifferentiation AT mishrasatyendrakumar homliealgebrasandhomliegroupsintegrationanddifferentiation AT shengyunhe homliealgebrasandhomliegroupsintegrationanddifferentiation |