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dc.contributor.authorEtingof, Pavel I.
dc.contributor.authorSchedler, Travis
dc.date.accessioned2011-05-19T19:41:07Z
dc.date.available2011-05-19T19:41:07Z
dc.date.issued2010-10
dc.identifier.issn1016-443X
dc.identifier.urihttp://hdl.handle.net/1721.1/62847
dc.description.abstractTo every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson traces on X, i.e. distributions invariant under Hamiltonian flow. When X has finitely many symplectic leaves, we prove that M(X) is holonomic. Thus, when X is affine and has finitely many symplectic leaves, the space of Poisson traces on X is finite-dimensional. More generally, to any morphism [phi]: X → Y and any quasicoherent sheaf of Poisson modules N on X, we attach a right D-module M [subscript phi] (X,N)M(XN) on X, and prove that it is holonomic if X has finitely many symplectic leaves, [phi] is finite, and N is coherent. As an application, we deduce that noncommutative filtered algebras, for which the associated graded algebra is finite over its center whose spectrum has finitely many symplectic leaves, have finitely many irreducible finite-dimensional representations. The appendix, by Ivan Losev, strengthens this to show that, in such algebras, there are finitely many prime ideals, and they are all primitive. This includes symplectic reflection algebras. Furthermore, we describe explicitly (in the settings of affine varieties and compact C ∞-manifolds [C superscript infinity symbol -manifolds]) the finite-dimensional space of Poisson traces on X when X = V/G, where V is symplectic and G is a finite group acting faithfully on V.en_US
dc.language.isoen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00039-010-0085-4en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceProf. Etingof via Michael Noga (arXiv ms.)en_US
dc.titlePOISSON TRACES AND D-MODULES ON POISSON VARIETIESen_US
dc.typeArticleen_US
dc.identifier.citationEtingof, Pavel, and Travis Schedler. “Poisson Traces and D-Modules on Poisson Varieties.” Geometric And Functional Analysis 20.4 (2010) : 958-987-987. Copyright © 2010, Springeren_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.approverEtingof, Pavel I.
dc.contributor.mitauthorEtingof, Pavel I.
dc.contributor.mitauthorSchedler, Travis
dc.relation.journalGeometric and Functional Analysisen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsEtingof, Pavel; Schedler, Travisen
dc.identifier.orcidhttps://orcid.org/0000-0002-0710-1416
mit.licenseOPEN_ACCESS_POLICYen_US
mit.metadata.statusComplete


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