Unimodularity criteria for Poisson structures on foliated manifolds
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DOI: 10.1007/s11005-017-1014-3
Abstract: We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria for… read more here.
Keywords: structures foliated; class; poisson; poisson structures ... See more keywords
Fiber-wise linear Poisson structures related to W∗-algebras
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2017.09.012
Abstract: Abstract In the framework of Banach differential geometry we investigate the fiber-wise linear Poisson structures as well as the Lie groupoid and Lie algebroid structures which are defined in the canonical way by the structure… read more here.
Keywords: linear poisson; fiber wise; wise linear; poisson ... See more keywords
Quasi-Poisson structures on moduli spaces of quasi-surfaces
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2020.103743
Abstract: Abstract In generalization of the classical Atiyah–Bott Poisson brackets on the moduli spaces of surfaces we define quasi-Poisson brackets on the moduli spaces of quasi-surfaces. read more here.
Keywords: poisson structures; quasi poisson; quasi surfaces; structures moduli ... See more keywords
Recurrence relations for symplectic realization of (quasi)-Poisson structures
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Physics A: Mathematical and Theoretical"
DOI: 10.1088/1751-8121/ab10e8
Abstract: It is known that any Poisson manifold can be embedded into a bigger space which admites a description in terms of the canonical Poisson structure, i.e., Darboux coordinates. Such a procedure is known as a… read more here.
Keywords: symplectic realization; poisson; poisson structures; poisson structure ... See more keywords
Shifted Poisson structures and deformation quantization
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DOI: 10.1112/topo.12012
Abstract: This paper is a sequel to [PTVV]. We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and poly-vector fields. We then introduce the formalism of formal… read more here.
Keywords: poisson structures; deformation quantization; shifted poisson; structures deformation ... See more keywords