Differential graded division algebras, their modules, and dg-simple algebras
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909349289394176 |
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| author | Zimmermann, Alexander |
| author_facet | Zimmermann, Alexander |
| contents | We give the definition of a dg-division algebra, that is a concept of a differential graded algebra which may serve as an analogue of a division algebra. We classify them completely, and show that they are either acyclic or have differential $0$. Further, we prove that the graded centre of dg-simple dg-algebras is a dg-division algebra, and also the dg-endomorphism ring of a dg-simple module is a dg-division algebra. We also shall give a Jacobson-Chevalley density theorem for acyclic dg-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential graded division algebras, their modules, and dg-simple algebras Zimmermann, Alexander Rings and Algebras Representation Theory 16E45 We give the definition of a dg-division algebra, that is a concept of a differential graded algebra which may serve as an analogue of a division algebra. We classify them completely, and show that they are either acyclic or have differential $0$. Further, we prove that the graded centre of dg-simple dg-algebras is a dg-division algebra, and also the dg-endomorphism ring of a dg-simple module is a dg-division algebra. We also shall give a Jacobson-Chevalley density theorem for acyclic dg-algebras. |
| title | Differential graded division algebras, their modules, and dg-simple algebras |
| topic | Rings and Algebras Representation Theory 16E45 |
| url | https://arxiv.org/abs/2408.05550 |