Extension, deformation and categorification of $\text{AssDer}$ pairs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866918158310309888 |
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| author | Das, Apurba Mandal, Ashis |
| author_facet | Das, Apurba Mandal, Ashis |
| contents | In this paper, we consider associative algebras equipped with derivations. A pair consisting of an associative algebra and a distinguished derivation is called an AssDer pair. We study central extensions and formal one-parameter deformations of AssDer pairs in terms of cohomology. Finally, we define $2$-derivations on associative $2$-algebras and show that the category of associative $2$-algebras with $2$-derivations is equivalent to the category of $2$-term $A_\infty$-algebras with homotopy derivations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_11415 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Extension, deformation and categorification of $\text{AssDer}$ pairs Das, Apurba Mandal, Ashis Rings and Algebras K-Theory and Homology Representation Theory 16E40, 16S80, 16W25, 18N25, 18N40 In this paper, we consider associative algebras equipped with derivations. A pair consisting of an associative algebra and a distinguished derivation is called an AssDer pair. We study central extensions and formal one-parameter deformations of AssDer pairs in terms of cohomology. Finally, we define $2$-derivations on associative $2$-algebras and show that the category of associative $2$-algebras with $2$-derivations is equivalent to the category of $2$-term $A_\infty$-algebras with homotopy derivations. |
| title | Extension, deformation and categorification of $\text{AssDer}$ pairs |
| topic | Rings and Algebras K-Theory and Homology Representation Theory 16E40, 16S80, 16W25, 18N25, 18N40 |
| url | https://arxiv.org/abs/2002.11415 |