An operadic approach to vertex algebra and Poisson vertex algebra cohomology
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.08754
 Bibcode:
 2018arXiv180608754B
 Keywords:

 Mathematics  Representation Theory;
 Mathematical Physics;
 17B69 (Primary);
 18D50;
 17B65;
 17B63;
 17B80 (Secondary)
 EPrint:
 72 pages, in the second version we corrected the part related to the cohomology of the free boson (Sec.11.3) and some other minor errors