Rota--Baxter operators on vertex algebras in integrated $λ$-bracket formalism and their associated 2-cocycles
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917525179072512 |
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| author | Alhussein, Hassan |
| author_facet | Alhussein, Hassan |
| contents | We study Rota--Baxter operators on vertex algebras using the integrated $λ$-bracket formalism. A Rota--Baxter operator produces a deformed vertex algebra structure, and the difference between the deformed and original brackets yields a two-cocycle in vertex algebra cohomology. This generalizes the classical relation between Rota--Baxter operators and Hochschild two-cocycles. We also characterize when this two-cocycle is trivial, showing that non-scalar operators give rise to non-trivial cohomology classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23799 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rota--Baxter operators on vertex algebras in integrated $λ$-bracket formalism and their associated 2-cocycles Alhussein, Hassan Quantum Algebra Rings and Algebras We study Rota--Baxter operators on vertex algebras using the integrated $λ$-bracket formalism. A Rota--Baxter operator produces a deformed vertex algebra structure, and the difference between the deformed and original brackets yields a two-cocycle in vertex algebra cohomology. This generalizes the classical relation between Rota--Baxter operators and Hochschild two-cocycles. We also characterize when this two-cocycle is trivial, showing that non-scalar operators give rise to non-trivial cohomology classes. |
| title | Rota--Baxter operators on vertex algebras in integrated $λ$-bracket formalism and their associated 2-cocycles |
| topic | Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2605.23799 |