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
Дата:2020
Автори: Jiang, Jun, Mishra, Satyendra Kumar, Sheng, Yunhe
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2020
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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2026-03-15T08:37:29Z
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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