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Computation of cohomology of vertex algebras
Name
2002.03612.pdf
Description
Accepted version
Size
651.97 KB
Format
Adobe PDF
Checksum (MD5)
c93e85f64c8b4d74b2b31b9cba62a856
Author(s)
Bakalov, Bojko
De Sole, Alberto
Kac, Victor G
Date Issued
2021
Journal
Japanese Journal of Mathematics
Publisher
Springer Science and Business Media LLC
Version
Author's final manuscript
Abstract
© 2020, The Mathematical Society of Japan and Springer Japan KK, part of Springer Nature. We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct a spectral sequence relating them. Since in “good” cases the classical PVA cohomology coincides with the variational PVA cohomology and there are well-developed methods to compute the latter, this enables us to compute the cohomology of vertex algebras in many interesting cases. Finally, we describe a unified approach to integrability through vanishing of the first cohomology, which is applicable to both classical and quantum systems of Hamiltonian PDEs.
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
10.1007/s11537-020-2034-9
