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dc.contributor.authorDe Sole, Alberto
dc.contributor.authorKac, Victor
dc.date.accessioned2015-01-15T16:41:45Z
dc.date.available2015-01-15T16:41:45Z
dc.date.issued2012-04
dc.date.submitted2011-06
dc.identifier.issn0010-3616
dc.identifier.issn1432-0916
dc.identifier.urihttp://hdl.handle.net/1721.1/92882
dc.description.abstractIn our recent paper “The variational Poisson cohomology” (2011) we computed the dimension of the variational Poisson cohomology H[subscript K](V) for any quasiconstant coefficient ℓ × ℓ matrix differential operator K of order N with invertible leading coefficient, provided that V is a normal algebra of differential functions over a linearly closed differential field. In the present paper we show that, for K skewadjoint, the Z -graded Lie superalgebra H[subscript K](V) is isomorphic to the finite dimensional Lie superalgebra [˜ over H](Nℓ,S) . We also prove that the subalgebra of “essential” variational Poisson cohomology, consisting of classes vanishing on the Casimirs of K, is zero. This vanishing result has applications to the theory of bi-Hamiltonian structures and their deformations. At the end of the paper we consider also the translation invariant case.en_US
dc.description.sponsorshipNational Science Foundation (U.S.)en_US
dc.language.isoen_US
dc.publisherSpringer-Verlagen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00220-012-1461-8en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleEssential Variational Poisson Cohomologyen_US
dc.typeArticleen_US
dc.identifier.citationDe Sole, Alberto, and Victor G. Kac. “Essential Variational Poisson Cohomology.” Commun. Math. Phys. 313, no. 3 (April 3, 2012): 837–864.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorKac, Victoren_US
dc.relation.journalCommunications in Mathematical Physicsen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dspace.orderedauthorsDe Sole, Alberto; Kac, Victor G.en_US
dc.identifier.orcidhttps://orcid.org/0000-0002-2860-7811
mit.licenseOPEN_ACCESS_POLICYen_US


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