English

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 λ\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.

Keywords

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}
}