Representations and cohomologies of modified λ-differential Hom-Lie algebras
In this paper, we introduce the concept and representations of modified $ \lambda $-differential Hom-Lie algebras. We then develop the cohomology of modified $ \lambda $-differential Hom-Lie algebras with coefficients in a suitable representation. As applications, abelian extensions and skeletal mod...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024213?viewType=HTML |
| _version_ | 1797323859157843968 |
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| author | Yunpeng Xiao Wen Teng |
| author_facet | Yunpeng Xiao Wen Teng |
| author_sort | Yunpeng Xiao |
| collection | DOAJ |
| description | In this paper, we introduce the concept and representations of modified $ \lambda $-differential Hom-Lie algebras. We then develop the cohomology of modified $ \lambda $-differential Hom-Lie algebras with coefficients in a suitable representation. As applications, abelian extensions and skeletal modified $ \lambda $-differential Hom-Lie 2-algebras are characterized in terms of cohomology groups. |
| first_indexed | 2024-03-08T05:34:11Z |
| format | Article |
| id | doaj.art-a73e22f51cbb47f9ab6938347f4f66e8 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:34:11Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a73e22f51cbb47f9ab6938347f4f66e82024-02-06T01:17:13ZengAIMS PressAIMS Mathematics2473-69882024-01-01924309432510.3934/math.2024213Representations and cohomologies of modified λ-differential Hom-Lie algebrasYunpeng Xiao 0Wen Teng11. School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China2. School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, ChinaIn this paper, we introduce the concept and representations of modified $ \lambda $-differential Hom-Lie algebras. We then develop the cohomology of modified $ \lambda $-differential Hom-Lie algebras with coefficients in a suitable representation. As applications, abelian extensions and skeletal modified $ \lambda $-differential Hom-Lie 2-algebras are characterized in terms of cohomology groups.https://www.aimspress.com/article/doi/10.3934/math.2024213?viewType=HTMLhom-lie algebrasmodified $ \lambda $-differential operatorcohomologyextensionhom-lie 2-algebras |
| spellingShingle | Yunpeng Xiao Wen Teng Representations and cohomologies of modified λ-differential Hom-Lie algebras AIMS Mathematics hom-lie algebras modified $ \lambda $-differential operator cohomology extension hom-lie 2-algebras |
| title | Representations and cohomologies of modified λ-differential Hom-Lie algebras |
| title_full | Representations and cohomologies of modified λ-differential Hom-Lie algebras |
| title_fullStr | Representations and cohomologies of modified λ-differential Hom-Lie algebras |
| title_full_unstemmed | Representations and cohomologies of modified λ-differential Hom-Lie algebras |
| title_short | Representations and cohomologies of modified λ-differential Hom-Lie algebras |
| title_sort | representations and cohomologies of modified λ differential hom lie algebras |
| topic | hom-lie algebras modified $ \lambda $-differential operator cohomology extension hom-lie 2-algebras |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024213?viewType=HTML |
| work_keys_str_mv | AT yunpengxiao representationsandcohomologiesofmodifiedldifferentialhomliealgebras AT wenteng representationsandcohomologiesofmodifiedldifferentialhomliealgebras |