Title: Deformation Quantization of Poisson Structures Associated to Lie Algebroids
Authors: Neumaier, Nikolai ×
Waldmann, Stefan #
Issue Date: 2009
Publisher: Natl acad sci ukraine, inst math
Series Title: Symmetry, Integrability and Geometry: Methods and Applications vol:5 pages:-
Article number: 074
Abstract: In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E*, where E -> M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even symplectic, our construction gets along without Kontsevich's formality theorem but is based on a generalized Fedosov construction. As the whole construction merely uses geometric structures of E we also succeed in determining the dependence of the resulting star products on these data in finding appropriate equivalence transformations between them. Finally, the concreteness of the construction allows to obtain explicit formulas even for a wide class of derivations and self-equivalences of the products. Moreover, we can show that some of our products are in direct relation to the universal enveloping algebra associated to the Lie algebroid. Finally, we show that for a certain class of star products on E* the integration with respect to a density with vanishing modular vector field defines a trace functional.
ISSN: 1815-0659
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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