Cohomology and formal deformations of $n$-Hom–Lie color algebras
UDC 512.5 The aim of this paper is to provide a cohomology of $n$-Hom–Lie color algebras, in particular,  a cohomology governing one-parameter formal deformations.  Then we also study formal deformations of the $n$-Hom–Lie color algebras and introduce the notio...
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| Datum: | 2023 |
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Institute of Mathematics, NAS of Ukraine
2023
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512632889409536 |
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| author | Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. |
| author_facet | Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. |
| author_sort | Abdaoui, K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:34:38Z |
| description | UDC 512.5
The aim of this paper is to provide a cohomology of $n$-Hom–Lie color algebras, in particular,  a cohomology governing one-parameter formal deformations.  Then we also study formal deformations of the $n$-Hom–Lie color algebras and introduce the notion of Nijenhuis operator on a $n$-Hom–Lie color algebra, which may give rise to infinitesimally trivial $(n-1)$-order deformations.  Furthermore, in connection with Nijenhuis operators, we introduce and discuss the notion of product structure  on $n$-Hom–Lie color algebras. |
| doi_str_mv | 10.3842/umzh.v75i9.7238 |
| first_indexed | 2026-03-24T03:31:53Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7238 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:53Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-72382024-06-19T00:34:38Z Cohomology and formal deformations of $n$-Hom–Lie color algebras Cohomology and formal deformations of $n$-Hom–Lie color algebras Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. n-Hom-Lie color algebra UDC 512.5 The aim of this paper is to provide a cohomology of $n$-Hom–Lie color algebras, in particular,  a cohomology governing one-parameter formal deformations.  Then we also study formal deformations of the $n$-Hom–Lie color algebras and introduce the notion of Nijenhuis operator on a $n$-Hom–Lie color algebra, which may give rise to infinitesimally trivial $(n-1)$-order deformations.  Furthermore, in connection with Nijenhuis operators, we introduce and discuss the notion of product structure  on $n$-Hom–Lie color algebras. УДК 512.5 Когомології та формальні деформації алгебр кольорів $n$-Хома–Лі  Мета цієї статті – визначити когомологію  алгебри кольорів $n$-Хомa–Лі та, зокрема, когомологію, що керує формальними однопараметричними деформаціями. Крім того, вивчаються формальні деформації алгебри кольорів $n$-Хомa–Лі  та введено поняття оператора Нойєнгайса на алгебрі кольорів $n$-Хомa–Лі, що може привести до інфінітезимально тривіальної деформації $(n-1)$-го порядку. Крім того, у зв’язку з операторами Нойєнгайса введено та обговорено поняття структури добутку на алгебрах кольорів $n$-Хомa–Лі.  Institute of Mathematics, NAS of Ukraine 2023-09-26 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7238 10.3842/umzh.v75i9.7238 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 9 (2023); 1155 - 1177 Український математичний журнал; Том 75 № 9 (2023); 1155 - 1177 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7238/9744 Copyright (c) 2023 Abdenacer Makhlouf |
| spellingShingle | Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. Abdaoui, K. Gharbi, R. Mabrouk, S. Makhlouf, A. Cohomology and formal deformations of $n$-Hom–Lie color algebras |
| title | Cohomology and formal deformations of $n$-Hom–Lie color algebras |
| title_alt | Cohomology and formal deformations of $n$-Hom–Lie color algebras |
| title_full | Cohomology and formal deformations of $n$-Hom–Lie color algebras |
| title_fullStr | Cohomology and formal deformations of $n$-Hom–Lie color algebras |
| title_full_unstemmed | Cohomology and formal deformations of $n$-Hom–Lie color algebras |
| title_short | Cohomology and formal deformations of $n$-Hom–Lie color algebras |
| title_sort | cohomology and formal deformations of $n$-hom–lie color algebras |
| topic_facet | n-Hom-Lie color algebra |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7238 |
| work_keys_str_mv | AT abdaouik cohomologyandformaldeformationsofnhomliecoloralgebras AT gharbir cohomologyandformaldeformationsofnhomliecoloralgebras AT mabrouks cohomologyandformaldeformationsofnhomliecoloralgebras AT makhloufa cohomologyandformaldeformationsofnhomliecoloralgebras AT abdaouik cohomologyandformaldeformationsofnhomliecoloralgebras AT gharbir cohomologyandformaldeformationsofnhomliecoloralgebras AT mabrouks cohomologyandformaldeformationsofnhomliecoloralgebras AT makhloufa cohomologyandformaldeformationsofnhomliecoloralgebras |