Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures

Symmetry Integrability and Geometry-Methods and Applications

article

Stjepan Meljanac¹  Zoran Škoda² 

[1] Theoretical Physics Division, Institute Rudjer Bošković;Faculty of Science, University of Hradec Kr´alov´e

关键词: deformation quantization;    Hopf algebroid;    noncommutative phase space;    Drinfeld twist;    linear Poisson structure;   

DOI  :  10.3842/SIGMA.2018.026

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown