Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures
Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extendability of order deforma...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2022 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2022
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211733 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures. Meijun Liu, Jiefeng Liu and Yunhe Sheng. SIGMA 18 (2022), 054, 26 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862642508367921152 |
|---|---|
| author | Liu, Meijun Liu, Jiefeng Sheng, Yunhe |
| author_facet | Liu, Meijun Liu, Jiefeng Sheng, Yunhe |
| citation_txt | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures. Meijun Liu, Jiefeng Liu and Yunhe Sheng. SIGMA 18 (2022), 054, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extendability of order deformations to order + 1 deformations of relative Rota-Baxter operators in terms of this cohomology theory. We also construct a graded Lie algebra on the space of multi-derivations of a vector bundle whose Maurer-Cartan elements characterize left-symmetric algebroids. We show that there is a homomorphism from the controlling graded Lie algebra of relative Rota-Baxter operators on Lie algebroids to the controlling graded Lie algebra of left-symmetric algebroids. Consequently, there is a natural homomorphism from the cohomology groups of a relative Rota-Baxter operator to the deformation cohomology groups of the associated left-symmetric algebroid. As applications, we give the controlling graded Lie algebra and the cohomology theory of Koszul-Vinberg structures on left-symmetric algebroids.
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| first_indexed | 2026-03-15T07:47:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211733 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T07:47:38Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Liu, Meijun Liu, Jiefeng Sheng, Yunhe 2026-01-09T12:55:05Z 2022 Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures. Meijun Liu, Jiefeng Liu and Yunhe Sheng. SIGMA 18 (2022), 054, 26 pages 1815-0659 2020 Mathematics Subject Classification: 53D17; 53C25; 58A12; 17B70 arXiv:2108.08906 https://nasplib.isofts.kiev.ua/handle/123456789/211733 https://doi.org/10.3842/SIGMA.2022.054 Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extendability of order deformations to order + 1 deformations of relative Rota-Baxter operators in terms of this cohomology theory. We also construct a graded Lie algebra on the space of multi-derivations of a vector bundle whose Maurer-Cartan elements characterize left-symmetric algebroids. We show that there is a homomorphism from the controlling graded Lie algebra of relative Rota-Baxter operators on Lie algebroids to the controlling graded Lie algebra of left-symmetric algebroids. Consequently, there is a natural homomorphism from the cohomology groups of a relative Rota-Baxter operator to the deformation cohomology groups of the associated left-symmetric algebroid. As applications, we give the controlling graded Lie algebra and the cohomology theory of Koszul-Vinberg structures on left-symmetric algebroids. This research was supported by the National Key Research and Development Program of China (2021YFA1002000), the National Natural Science Foundation of China (11901501, 11922110), the China Postdoctoral Science Foundation (2021M700750), and the Fundamental Research Funds for the Central Universities (2412022QD033). We give our warmest thanks to the referees for their very useful comments that improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures Article published earlier |
| spellingShingle | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures Liu, Meijun Liu, Jiefeng Sheng, Yunhe |
| title | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures |
| title_full | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures |
| title_fullStr | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures |
| title_full_unstemmed | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures |
| title_short | Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures |
| title_sort | deformations and cohomologies of relative rota-baxter operators on lie algebroids and koszul-vinberg structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211733 |
| work_keys_str_mv | AT liumeijun deformationsandcohomologiesofrelativerotabaxteroperatorsonliealgebroidsandkoszulvinbergstructures AT liujiefeng deformationsandcohomologiesofrelativerotabaxteroperatorsonliealgebroidsandkoszulvinbergstructures AT shengyunhe deformationsandcohomologiesofrelativerotabaxteroperatorsonliealgebroidsandkoszulvinbergstructures |