2019 journal article
An operadic approach to vertex algebra and Poisson vertex algebra cohomology
JAPANESE JOURNAL OF MATHEMATICS, 14(2), 249–342.
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Source: Web Of Science
Added: October 7, 2019
We translate the construction of the chiral operad by Beilinson and Drinfeld to the purely algebraic language of vertex algebras. Consequently, the general construction of a cohomology complex associated to a linear operad produces a vertex algebra cohomology complex. Likewise, the associated graded of the chiral operad leads to a classical operad, which produces a Poisson vertex algebra cohomology complex. The latter is closely related to the variational Poisson cohomology studied by two of the authors.