A cohomology theory of supercommutative algebras and grading-restricted vertex superalgebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917029094621184 |
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| author | Johnson, Paul Qi, Fei |
| author_facet | Johnson, Paul Qi, Fei |
| contents | This paper constructs the cohomology theory for grading-restricted vertex superalgebras, generalizing Yi-Zhi Huang's cohomology theory of grading-restricted vertex algebras. To simplify the discussion, motivate the construction, and make it easier for the reader to understand the technical points, we also include the construction of the cohomology theory of supercommutative associative algebras, a generalization of the Harrison cohomology theory of a commutative algebra that has not been explicitly written down. The paper will serve as the foundation for many subsequent studies, especially, the deformation theory of vertex superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A cohomology theory of supercommutative algebras and grading-restricted vertex superalgebras Johnson, Paul Qi, Fei Quantum Algebra High Energy Physics - Theory This paper constructs the cohomology theory for grading-restricted vertex superalgebras, generalizing Yi-Zhi Huang's cohomology theory of grading-restricted vertex algebras. To simplify the discussion, motivate the construction, and make it easier for the reader to understand the technical points, we also include the construction of the cohomology theory of supercommutative associative algebras, a generalization of the Harrison cohomology theory of a commutative algebra that has not been explicitly written down. The paper will serve as the foundation for many subsequent studies, especially, the deformation theory of vertex superalgebras. |
| title | A cohomology theory of supercommutative algebras and grading-restricted vertex superalgebras |
| topic | Quantum Algebra High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.17293 |