Xu's quantization conjecture for Lie bialgebroids
Xu's quantization conjecture for Lie bialgebroids
Let be a Lie bialgebroid. A quantization is a topological deformation of the standard associative bialgebroid structure on the universal enveloping algebra , with , whose semiclassicalisation reproduces the given Lie bialgebroid structure; such a quantum object is called a quantum groupoid. Xu's conjecture. Every Lie bialgebroid admits a quantization as a quantum groupoid. Quantization is known for Lie bialgebroids associated with Poisson manifolds, regular triangular Lie algebroids, and generic triangular Lie bialgebroids, but the conjecture remains open for a generic Lie bialgebroid.
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Sources & referencesView supporting material
Primary source
Kevin Morand, “A Note on Multi-Oriented Graph Complexes and Deformation Quantization of Lie Bialgebroids”, arXiv:2102.07593 (2022).
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