Connections and naïve lifting of DG modules
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909994332454912 |
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| author | Nasseh, Saeed Ono, Maiko Yoshino, Yuji |
| author_facet | Nasseh, Saeed Ono, Maiko Yoshino, Yuji |
| contents | In this paper, we generalize the notion of connections, which was introduced by Alain Connes in noncommutative differential geometry, to the differential graded (DG) homological algebra setting. Then, along a DG algebra homomorphism $A \to B$, where $B$ is assumed to be projective as an underlying graded $A$-module, we give necessary and sufficient conditions for a semifree DG $B$-module to be naïvely liftable to $A$ in terms of connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Connections and naïve lifting of DG modules Nasseh, Saeed Ono, Maiko Yoshino, Yuji Commutative Algebra 13N15, 16E45, 16W25, 16W50, 16W80 In this paper, we generalize the notion of connections, which was introduced by Alain Connes in noncommutative differential geometry, to the differential graded (DG) homological algebra setting. Then, along a DG algebra homomorphism $A \to B$, where $B$ is assumed to be projective as an underlying graded $A$-module, we give necessary and sufficient conditions for a semifree DG $B$-module to be naïvely liftable to $A$ in terms of connections. |
| title | Connections and naïve lifting of DG modules |
| topic | Commutative Algebra 13N15, 16E45, 16W25, 16W50, 16W80 |
| url | https://arxiv.org/abs/2601.12550 |