Quantizability conjecture for Lie bialgebroids

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Let E→XE\to X be a Lie algebroid, and suppose its dual bundle E∗→XE^*\to X is also a Lie algebroid such that the differential dE∗d_{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.

References

Primary source

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

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