Hopf Algebroid Twists for Deformation Quantization of Linear Poisson Structures

Abstract

In our earlier article [Lett. Math. Phys. 107 (2017), 475-503, arXiv:1409.8188], 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.

References in corpus (3)

• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist

Cited by in corpus (5)

• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Remarks on simple interpolation between Jordanian twists
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces