Maurer-Cartan characterization and cohomology of compatible LieDer and AssDer pairs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912094437244928 |
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| author | Imed, Basdouri Salima, Ghribi Amin, Sadraoui Mohamed |
| author_facet | Imed, Basdouri Salima, Ghribi Amin, Sadraoui Mohamed |
| contents | A LieDer pair (respectively, an AssDer pair) is a Lie algebra equipped with a derivation (respectively, an associative algebra equipped with a derivation). A couple of LieDer pair structures on a vector space are called Compatible LieDer pairs (respectively, compatible AssDer pairs) if any linear combination of the underlying structure maps is still a LieDer pair (respectively, AssDer pair) structure. In this paper, we study compatible AssDer pairs, compatible LieDer pairs, and their cohomologies. We also discuss about other compatible structures such as compatible dendriform algebras with derivations, compatible zinbiel algebras with derivations, and compatible pre-LieDer pairs. We describe a relationship amongst these compatible structures using specific tools like Rota-Baxter operators, endomorphism operators, and the commutator bracket. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14015 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maurer-Cartan characterization and cohomology of compatible LieDer and AssDer pairs Imed, Basdouri Salima, Ghribi Amin, Sadraoui Mohamed Rings and Algebras A LieDer pair (respectively, an AssDer pair) is a Lie algebra equipped with a derivation (respectively, an associative algebra equipped with a derivation). A couple of LieDer pair structures on a vector space are called Compatible LieDer pairs (respectively, compatible AssDer pairs) if any linear combination of the underlying structure maps is still a LieDer pair (respectively, AssDer pair) structure. In this paper, we study compatible AssDer pairs, compatible LieDer pairs, and their cohomologies. We also discuss about other compatible structures such as compatible dendriform algebras with derivations, compatible zinbiel algebras with derivations, and compatible pre-LieDer pairs. We describe a relationship amongst these compatible structures using specific tools like Rota-Baxter operators, endomorphism operators, and the commutator bracket. |
| title | Maurer-Cartan characterization and cohomology of compatible LieDer and AssDer pairs |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2311.14015 |