Cohomologies and deformations of differential algebra morphisms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911793599741952 |
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| author | Du, Lei Bao, Yanhong |
| author_facet | Du, Lei Bao, Yanhong |
| contents | This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then, we prove the Cohomology Comparison Theorem of differential algebra morphisms, i.e., the cohomology of a morphism of differential algebras is isomorphic to the cohomology of an auxiliary differential algebra. Finally, we can give a minimal model for morphism of differential algebras with weight=0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07521 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomologies and deformations of differential algebra morphisms Du, Lei Bao, Yanhong Rings and Algebras This paper studies the formal deformations of differential algebra morphisms. As a consequence, we develop a cohomology theory of differential algebra morphisms to interpret the lower degree cohomology groups as formal deformations. Then, we prove the Cohomology Comparison Theorem of differential algebra morphisms, i.e., the cohomology of a morphism of differential algebras is isomorphic to the cohomology of an auxiliary differential algebra. Finally, we can give a minimal model for morphism of differential algebras with weight=0. |
| title | Cohomologies and deformations of differential algebra morphisms |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2403.07521 |