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Computation of cohomology of Lie conformal and Poisson vertex algebras

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 10 Jul 2020Embargo end date: 01 Jan 2019 United States, Italy English Publisher:Springer Science and Business Media LLCJournal:Selecta Mathematica, volume 26 (issn: 1022-1824, eissn: 1420-9020, Copyright policy )
Authors: Bakalov B.; De Sole A.; Kac V. G.;

doi: 10.1007/s00029-020-00578-2 , 10.48550/arxiv.1903.12059

arXiv: http://arxiv.org/abs/1903.12059

handle: 11573/1460512 , 1721.1/131571

Computation of cohomology of Lie conformal and Poisson vertex algebras

Abstract

We develop methods for computation of Poisson vertex algebra cohomology. This cohomology is computed for the free bosonic and fermionic Poisson vertex (super)algebras, as well as for the universal affine and Virasoro Poisson vertex algebras. We establish finite dimensionality of this cohomology for conformal Poisson vertex (super)algebras that are finitely and freely generated by elements of positive conformal weight.

42 pages, revised version with some notational changes

Countries
United States, Italy
Related Organizations
Keywords

FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Representation Theory (math.RT), Primary 17B69, Secondary 17B56, 17B63, Affine Lie algebras; basic cohomology; energy operator; LCA cohomology; Lie conformal (super)algebras; poisson vertex (super)algebras; variational PVA cohomology; virasoro algebra, Mathematics - Representation Theory, Mathematical Physics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Top 10%
Top 10%
Top 10%
Green
bronze