The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras
The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploits strongly the Hom-type structure and fits perfectly with simultaneous deformations of the multiplication and the homomorphism defin...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-05-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022141?viewType=HTML |
| _version_ | 1797989507516071936 |
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| author | Shanshan Liu Abdenacer Makhlouf Lina Song |
| author_facet | Shanshan Liu Abdenacer Makhlouf Lina Song |
| author_sort | Shanshan Liu |
| collection | DOAJ |
| description | The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploits strongly the Hom-type structure and fits perfectly with simultaneous deformations of the multiplication and the homomorphism defining a Hom-pre-Lie algebra. Moreover, we show that its second cohomology group classifies abelian extensions of a Hom-pre-Lie algebra by a representation. |
| first_indexed | 2024-04-11T08:21:26Z |
| format | Article |
| id | doaj.art-7df6d0da852146babcee5560ffbd6565 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-11T08:21:26Z |
| publishDate | 2022-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-7df6d0da852146babcee5560ffbd65652022-12-22T04:34:57ZengAIMS PressElectronic Research Archive2688-15942022-05-013082748277310.3934/era.2022141The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebrasShanshan Liu 0Abdenacer Makhlouf1Lina Song21. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China2. University of Haute Alsace, IRIMAS-Mathematics department, Mulhouse, France3. Department of Mathematics, Jilin University, Changchun 130012, Jilin, ChinaThe main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploits strongly the Hom-type structure and fits perfectly with simultaneous deformations of the multiplication and the homomorphism defining a Hom-pre-Lie algebra. Moreover, we show that its second cohomology group classifies abelian extensions of a Hom-pre-Lie algebra by a representation.https://www.aimspress.com/article/doi/10.3934/era.2022141?viewType=HTMLhom-pre-lie algebracohomologyabelian extensionformal deformation |
| spellingShingle | Shanshan Liu Abdenacer Makhlouf Lina Song The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras Electronic Research Archive hom-pre-lie algebra cohomology abelian extension formal deformation |
| title | The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras |
| title_full | The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras |
| title_fullStr | The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras |
| title_full_unstemmed | The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras |
| title_short | The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras |
| title_sort | full cohomology abelian extensions and formal deformations of hom pre lie algebras |
| topic | hom-pre-lie algebra cohomology abelian extension formal deformation |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022141?viewType=HTML |
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