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.
- Pub Date:
- June 2018
- Mathematics - Representation Theory;
- Mathematical Physics;
- 17B69 (Primary);
- 17B80 (Secondary)
- 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