The Van den Bergh duality and the modular symmetry of a Poisson variety

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dc.creatorDolgushev, Vasiliy
dc.date2006-12-11
dc.date2007-07-31
dc.date.accessioned2026-07-07T08:21:12Z
dc.date.available2026-07-07T08:21:12Z
dc.descriptionWe consider a smooth Poisson affine variety with the trivial canonical bundle over complex numbers. For such a variety the deformation quantization algebra A_h enjoys the conditions of the Van den Bergh duality theorem and the corresponding dualizing module is determined by an outer automorphism of A_h intrinsic to A_h. We show how this automorphism can be expressed in terms of the modular class of the corresponding Poisson variety. We also prove that the Van den Bergh dualizing module of the deformation quantization algebra A_h is free if and only if the corresponding Poisson structure is unimodular.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/math/0612288
dc.identifierhttp://arxiv.org/abs/math/0612288
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/135282
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectK-Theory and Homology
dc.titleThe Van den Bergh duality and the modular symmetry of a Poisson variety
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