Rota--Baxter operators on vertex algebras in integrated $\lambda$-bracket formalism and their associated 2-cocycles
Quantum Algebra
2026-05-25 v1 Rings and Algebras
Abstract
We study Rota--Baxter operators on vertex algebras using the integrated -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.
Cite
@article{arxiv.2605.23799,
title = {Rota--Baxter operators on vertex algebras in integrated $\lambda$-bracket formalism and their associated 2-cocycles},
author = {Hassan Alhussein},
journal= {arXiv preprint arXiv:2605.23799},
year = {2026}
}