Operad and cohomology of associative algebras with generalized derivations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911979186159616 |
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| author | Xu, Jiang-Nan Bao, Yan-Hong |
| author_facet | Xu, Jiang-Nan Bao, Yan-Hong |
| contents | An associative algebra with a generalized derivation is called an AsGDer triple. We introduce the operad that encodes AsGDer triples, and prove it is a Koszul operad. Using its Koszul dual cooperad, we introduce the homotopy version of AsGDer triples. As an application, we construct the AsGDer cohomology theory for AsGDer triples, and show that the formal deformation of an AsGDer triple is controlled by the AsGDer cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operad and cohomology of associative algebras with generalized derivations Xu, Jiang-Nan Bao, Yan-Hong Rings and Algebras 16R10, 16R99, 18M60 An associative algebra with a generalized derivation is called an AsGDer triple. We introduce the operad that encodes AsGDer triples, and prove it is a Koszul operad. Using its Koszul dual cooperad, we introduce the homotopy version of AsGDer triples. As an application, we construct the AsGDer cohomology theory for AsGDer triples, and show that the formal deformation of an AsGDer triple is controlled by the AsGDer cohomology. |
| title | Operad and cohomology of associative algebras with generalized derivations |
| topic | Rings and Algebras 16R10, 16R99, 18M60 |
| url | https://arxiv.org/abs/2407.19298 |