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arXiv · 2605.23799

Rota-Baxter Operators on Vertex Algebras in Integrated $\lambda$-Bracket Formalism and Their Associated 2-Cocycles

Hassan Alhussein
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Abstract

We study Rota--Baxter operators on vertex algebras using the integrated $\lambda$-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.

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BibTeXRIS

Hassan Alhussein. 2026-05-22. Rota-Baxter Operators on Vertex Algebras in Integrated $\lambda$-Bracket Formalism and Their Associated 2-Cocycles. https://arxiv.org/abs/2605.23799

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