Quantizability conjecture for Lie bialgebroids

Let EXE\to X be a Lie algebroid, and suppose its dual bundle EXE^*\to X is also a Lie algebroid such that the differential dEd_{E^*} on Γ(X,E)\Gamma(X,\wedge^*E) is a derivation of the super-bracket on EE. Call EE a Lie bialgebroid. It is quantizable if there exists a deformation of its universal enveloping algebra UEUE whose semi-classical limit is precisely the given Lie bialgebroid structure.

Quantizability conjecture. Any Lie bialgebroid is quantizable.

This asserts the existence of a deformation quantization for every Lie bialgebroid. The supplied text gives no evidence that the assertion has been proved or disproved, so its status remains open.

Sources & referencesView supporting material

Primary source

Damien Calaque, “Formality for Lie algebroids”, arXiv:math/0404265 (2004).

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