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Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018) Cet article a éte moissonné depuis la source Math-Net.Ru

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In our earlier article [Lett. Math. Phys. 107 (2017), 475–503], we explicitly described a topological Hopf algebroid playing the role of the noncommutative phase space of Lie algebra type. Ping Xu has shown that every deformation quantization leads to a Drinfeld twist of the associative bialgebroid of $h$-adic series of differential operators on a fixed Poisson manifold. In the case of linear Poisson structures, the twisted bialgebroid essentially coincides with our construction. Using our explicit description of the Hopf algebroid, we compute the corresponding Drinfeld twist explicitly as a product of two exponential expressions.
Keywords: deformation quantization; Hopf algebroid; noncommutative phase space; Drinfeld twist; linear Poisson structure. 
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     author = {Stjepan Meljanac and Zoran \v{S}koda},
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Stjepan Meljanac; Zoran Škoda. Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a25/

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