This article is cited in 4 papers

Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures

Stjepan Meljanac^a, Zoran Škoda<sup>bc

a</sup> Theoretical Physics Division, Institute Rudjer Bošković, Bijenička cesta 54, P.O. Box 180, HR-10002 Zagreb, Croatia
^b University of Zadar, Department of Teachers’ Education, Franje Tudjmana 24, 23000 Zadar, Croatia
^c Faculty of Science, University of Hradec Králové, Rokitanského 62, Hradec Králové, Czech Republic

Abstract: 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.

MSC: 53D55; 16S30; 16T05

Received: May 24, 2017; in final form March 13, 2018; Published online March 25, 2018

Language: English

DOI: 10.3842/SIGMA.2018.026

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