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 e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.08754
- arXiv:
- arXiv:1806.08754
- Bibcode:
- 2018arXiv180608754B
- Keywords:
-
- Mathematics - Representation Theory;
- Mathematical Physics;
- 17B69 (Primary);
- 18D50;
- 17B65;
- 17B63;
- 17B80 (Secondary)
- E-Print:
- 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